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In his celebrated paper Generic projections, John Mather has shown that almost all linear projections from a submanifold of a vector space into a subspace are transverse with respect to a given modular submanifold. In this paper, an improvement of Mather's result is stated. Namely, we show that almost all linear perturbations of a smooth mapping from a submanifold of ℝm into ℝℓ yield a transverse mapping with respect to a given modular submanifold. Moreover, applications of this result are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the valency of planar harmonic mappings of bounded boundary rotation of the open unit disc D. The paper is motivated by the earlier work of the first two authors [Complex Analysis Oper. Theory 5 (2011), 767-774] and the recent work of T. Hayami [Complex Var. Elliptic Equ. 59 (2014), 1214-1222]. First, the authors give a counterexample showing that both the main result of Hayami, Theorem 2.1, and the related conjecture, Conjecture 4.1, are false. Second, the authors give a valency criterion for planar harmonic mappings of bounded boundary rotation of D, proving an ameliorated statement of Theorem 2.1 and settling a modified version of Conjecture 4.1. [ABSTRACT FROM AUTHOR]

It is due to Milnor that there is no Herman ring for any rational map with two critical values. In this paper, we are concerned with if there exist Herman rings for rational maps with three critical values. We first prove that such rational maps cannot have Herman rings of period 1, 2, or 3. Then we prove all regularly ramified rational maps have no Herman rings in their Fatou sets. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. The first purpose is to establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into an arbitrary projective variety intersecting a family of hypersurfaces in subgeneral position. In our result, the truncation level of the counting functions is estimated explicitly. Our result is an extension of the classical second main theorem of H. Cartan and is also a generalization of the recent second main theorem of M. Ru and improves some recent results. The second purpose of this paper is to give another proof for the second main theorem for the special case where the projective variety is a projective space, by which the truncation level of the counting functions is estimated better than that of the general case. [ABSTRACT FROM AUTHOR]

We consider the iteration of quasiregular maps of transcendental type from Rd to Rd. In particular we study quasi-Fatou components, which are defined as the connected components of the complement of the Julia set. Many authors have studied the components of the Fatou set of a transcendental entire function, and our goal in this paper is to generalise some of these results to quasi-Fatou components. First, we study the number of complementary components of quasi-Fatou components, generalising, and slightly strengthening, a result of Kisaka and Shishikura. Second, we study the size of quasi-Fatou components that are bounded and have a bounded complementary component. We obtain results analogous to those of Zheng, and of Bergweiler, Rippon and Stallard. These are obtained using techniques which may be of interest even in the case of transcendental entire functions. [ABSTRACT FROM AUTHOR]

In the present paper, we prove the following result generalizing some well-known related results about biholomorphic or proper holomorphic mappings between some special domains in Cn. Let G1 and G2 be two compact Lie groups, which act linearly on Cn with O(Cn)Gj = C for j = 1, 2. Let 0 ∊ Ωj be bounded Gj -invariant domains in Cn for j = 1, 2. If f : Ω1 → Ω2 is a proper holomorphic mapping, then f extends holomorphically to an open neighborhood of Ω1, and in addition if f-1(0) = {0}, then f is a polynomial mapping. We also prove that if 0 ∊ Ω is a G1-invariant pseudoconvex domain in Cn with O(Cn)G1 = C, then Ω is orbit convex. The second result is used to prove the first one. [ABSTRACT FROM AUTHOR]

Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichmüller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal Teichmüller map between Riemann surfaces of finite type are theoretically guaranteed (see Fletcher and Markovic, Quasiconformal maps and Teichmüller theory, Oxford Graduate Texts in Math., vol. 11, Oxford University Press, Oxford, 2007). Recently, a simple iterative algorithm for computing the Teichmüller maps between connected Riemann surfaces with given boundary value was proposed by Lui, Lam, Yau, and Gu in Teichmüller extremal mapping and its applications to landmark matching registration, arXiv:1211.2569. Numerical results were reported in the paper to show the effectiveness of the algorithm. The method was successfully applied to landmarkmatching registration. The purpose of this paper is to prove the iterative algorithm proposed in loc. cit., indeed converges. [ABSTRACT FROM AUTHOR]

This is a paper with two aims. First, we show that the map from Z/pZ to itself defined by exponentiation x → mx has few 3-cycles—that is to say, the number of cycles of length 3 is o(p). This improves on previous bounds. Our second objective is to contribute to an ongoing discussion on how to find a nonsofic group. In particular, we show that, if the Higman group were sofic, there would be a map from Z/pZ to itself, locally like an exponential map, yet satisfying a recurrence property. [ABSTRACT FROM AUTHOR]

In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches. [ABSTRACT FROM AUTHOR]

In this paper we consider homeomorphisms of the torus ℝ2/ℤ2, homotopic to the identity, and their rotation sets. Let f be such a homeomorphism, ...: ℝ2 → ℝ2 be a fixed lift and ρ(...) ⊂ ℝ2 be its rotation set, which we assume to have interior. We also assume that the frontier of ρ(...) contains a rational vector ρ ∈ ℚ2 and we want to understand how stable this situation is. To be more precise, we want to know if it is possible to find two different homeomorphisms f1 and f2, arbitrarily small C0-perturbations of f, in a way that ρ does not belong to the rotation set of ... but belongs to the interior of the rotation set of ..., where ... and ... are the lifts of f1 and f2 that are close to .... We give two examples where this happens, supposing ρ = (0, 0). The first one is a smooth diffeomorphism with a unique fixed point lifted to a fixed point of .... The second one is an area preserving version of the first one, but in this conservative setting we only obtain a C0 example. We also present two theorems in the opposite direction. The first one says that if f is area preserving and analytic, we cannot find f1 and f2 as above. The second result, more technical, implies that the same statement holds if f belongs to a generic one parameter family (ft)t∈[0,1] of C2-diffeomorphisms of T2 (in the sense of Brunovsky). In particular, lifting our family to a family ... of plane diffeomorphisms, one deduces that if there exists a rational vector ρ and a parameter t∗ ∈ (0, 1) such that ρ(...) has non-empty interior, and ρ ∉ ρ(...) for t < t∗ close to t∗, then ρ ∉ int(ρ(...)) for all t > t∗ close to t∗. This kind of result reveals some sort of local stability of the rotation set near rational vectors of its boundary. [ABSTRACT FROM AUTHOR]

The main results of the paper concern the existence of fixed points of nonlinear F-contraction and the sum of this type of mapping with a compact operator. The results of Krasnosel’skii type are obtained with a usage of the Hausdorff measure of noncompactness and condensing mappings. The presented new tools give the possibility to verify the existence problems of the solutions for some classes of integral equations. [ABSTRACT FROM AUTHOR]

Let S be an orientable surface with negative Euler characteristic. For k ∈ N, let Ck(S) denote the k-curve graph, whose vertices are isotopy classes of essential simple closed curves on S and whose edges correspond to pairs of curves that can be realized to intersect at most k times. The theme of this paper is that the geometry of Teichmüller space and of the mapping class group captures local combinatorial properties of Ck(S), for large k. Using techniques for measuring distance in Teichmüller space, we obtain upper bounds on the following three quantities for large k: the clique number of Ck(S) (exponential in k, which improves on previous bounds of Juvan, Malnič, and Mobar and Przytycki); the maximum size of the intersection, whenever it is finite, of a pair of links in Ck (quasi-polynomial in k); and the diameter in C0(S) of a large clique of Ck(S) (uniformly bounded). As an application, we obtain quasi-polynomial upper bounds, depending only on the topology of S, on the number of short simple closed geodesics on any unit-square tiled surface homeomorphic to S. [ABSTRACT FROM AUTHOR]

We work over an algebraically closed field of characteristic zero. The purpose of this paper is to characterize a nondegenerate projective variety X with a linear projection which induces a nonbirational map to its image. As an application, for smooth X of degree d and codimension e, we prove the "semiampleness" of the (d - e + 1)th twist of the ideal sheaf. This improves a linear bound of the regularity of smooth projective varieties by Bayer-Mumford-Bertram-Ein-Lazarsfeld, and gives an asymptotic regularity bound. [ABSTRACT FROM AUTHOR]

Let G be a reductive complex Lie group acting holomorphically on Stein manifolds X and Y. Let pX : X → QX and pY : Y → QY be the quotient mappings. When is there an equivariant biholomorphism of X and Y ? A necessary condition is that the categorical quotients QX and QY are biholomorphic and that the biholomorphism φ sends the Luna strata of QX isomorphically onto the corresponding Luna strata of QY . Fix φ. We demonstrate two homotopy principles in this situation. The first result says that if there is a G-diffeomorphism Φ: X → Y , inducing φ, which is G-biholomorphic on the reduced fibres of the quotient mappings, then Φ is homotopic, through G-diffeomorphisms satisfying the same conditions, to a G-equivariant biholomorphism from X to Y . The second result roughly says that if we have a G-homeomorphism Φ: X → Y which induces a continuous family of Gequivariant biholomorphisms of the fibres pX -1(q) and pY -1(φ(q)) for q ∊ QX and if X satisfies an auxiliary property (which holds for most X), then Φ is homotopic, through G-homeomorphisms satisfying the same conditions, to a G-equivariant biholomorphism from X to Y . Our results improve upon those of our earlier paper. [ABSTRACT FROM AUTHOR]

Entrywise functions preserving the cone of positive semidefinite matrices have been studied by many authors, most notably by Schoenberg [Duke Math. J. 9, 1942] and Rudin [Duke Math. J. 26, 1959]. Following their work, it is well-known that entrywise functions preserving Loewner positivity in all dimensions are precisely the absolutely monotonic functions. However, there are strong theoretical and practical motivations to study functions preserving positivity in a fixed dimension n. Such characterizations for a fixed value of n are difficult to obtain, and in fact are only known in the 2 × 2 case. In this paper, using a novel and intuitive approach, we study entrywise functions preserving positivity on distinguished submanifolds inside the cone obtained by imposing rank constraints. These rank constraints are prevalent in applications, and provide a natural way to relax the elusive original problem of preserving positivity in a fixed dimension. In our main result, we characterize entrywise functions mapping n × n positive semidefinite matrices of rank at most l into positive semidefinite matrices of rank at most k for 1 ≥ l ≥ n and 1 ≥ k < n. We also demonstrate how an important necessary condition for preserving positivity by Horn and Loewner [Trans. Amer. Math. Soc. 136, 1969] can be significantly generalized by adding rank constraints. Finally, our techniques allow us to obtain an elementary proof of the classical characterization of functions preserving positivity in all dimensions obtained by Schoenberg and Rudin. [ABSTRACT FROM AUTHOR]

Slice regular functions have been extensively studied over the past decade, but much less is known about their boundary behavior. In this paper, we initiate the study of Julia theory for slice regular functions. More specifically, we establish the quaternionic versions of the Julia lemma, the Julia-Carathéodory theorem, the boundary Schwarz lemma, and the Burns-Krantz rigidity theorem for slice regular self-mappings of the open unit ball B and of the right half-space H+. Our quaternionic boundary Schwarz lemma involves a Lie bracket reflecting the non-commutativity of quaternions. Together with some explicit examples, it shows that the slice derivative of a slice regular self-mapping of B at a boundary fixed point is not necessarily a positive real number, in contrast to that in the complex case, meaning that its commonly believed version turns out to be totally wrong. [ABSTRACT FROM AUTHOR]

In this paper, we study the intersection of an entire holomorphic mapping and a complex Monge-Ampère current with a bounded potential. By using our results, we show a sufficient condition involving order functions of an entire holomorphic mapping such that the complement of its image is a pluripolar set. [ABSTRACT FROM AUTHOR]

Isogenies are the morphisms between elliptic curves and are, accordingly, a topic of interest in the subject. As such, they have been well studied, and have been used in several cryptographic applications. V'elu's formulas show how to explicitly evaluate an isogeny, given a specification of the kernel as a list of points. However, V'elu's formulas only work for elliptic curves specified by a Weierstrass equation. This paper presents formulas similar to V'elu's that can be used to evaluate isogenies on Edwards curves and Huff curves, which are normal forms of elliptic curves that provide an alternative to the traditional Weierstrass form. Our formulas are not simply compositions of V'elu's formulas with mappings to and from Weierstrass form. Our alternate derivation yields efficient formulas for isogenies with lower algebraic complexity than such compositions. In fact, these formulas have lower algebraic complexity than V'elu's formulas on Weierstrass curves. [ABSTRACT FROM AUTHOR]

This paper is an attempt to unify the multivariable operator model theory for ball-like domains and commutative polydiscs and extend it to a more general class of noncommutative polydomains Dqm (H) in B(H)n. An important role in our study is played by noncommutative Berezin transforms associated with the elements of the polydomain. These transforms are used to prove that each such polydomain has a universal model W = {Wi,j} consisting of weighted shifts acting on a tensor product of full Fock spaces. We introduce the noncommutative Hardy algebra F∞(Dqm ) as the weakly closed algebra generated by {Wi,j} and the identity, and use it to provide a WOT-continuous functional calculus for completely non-coisometric tuples in Dqm (H). It is shown that the Berezin transform is a completely isometric isomorphism between F∞(Dqm ) and the algebra of bounded free holomorphic functions on the radial part of Dqm (H). A characterization of the Beurling type joint invariant subspaces under {Wi,j} is also provided. It has been an open problem for quite some time to find significant classes of elements in the commutative polydisc for which a theory of characteristic functions and model theory can be developed along the lines of the Sz.-Nagy-Foias theory of contractions. We give a positive answer to this question, in our more general setting, providing a characterization for the class of tuples of operators in Dqm (H) which admit characteristic functions. The characteristic function is constructed explicitly as an artifact of the noncommutative Berezin kernel associated with the polydomain, and it is proved to be a complete unitary invariant for the class of completely non-coisometric tuples. Using noncommutative Berezin transforms and C*-algebra techniques, we develop a dilation theory on the noncommutative polydomain Dqm (H). [ABSTRACT FROM AUTHOR]

Certain classes of 3-manifolds, following Thurston, give rise to a 'skinning map', a self-map of the Teichmüller space of the boundary. This paper examines the skinning map of a 3-manifold M, a genus-2 handlebody with two rank-1 cusps. We exploit an orientation-reversing isometry of M to conclude that the skinning map associated to M sends a specified path to itself and use estimates on extremal length functions to show non-monotonicity and the existence of a critical point. A family of finite covers of M produces examples of non-immersion skinning maps on the Teichmüller spaces of surfaces in each even genus, and with either 4 or 6 punctures. [ABSTRACT FROM AUTHOR]

In this paper we study the harmonic elements of (convolution) Markov maps associated to (ergodic) actions of locally compact quantum groups on (σ-finite) von Neumann algebras. We give several equivalent conditions under which the harmonic elements are trivial. [ABSTRACT FROM AUTHOR]

In this paper, certain connections between complex symmetric operators and anti-automorphisms of singly generated C*-algebras are established. This provides a C*-algebra approach to the norm closure problem for complex symmetric operators. For T ∈ B(H) satisfying C*(T)∩K(H) = {0}, we give several characterizations for T to be a norm limit of complex symmetric operators. As applications, we give concrete characterizations for weighted shifts with nonzero weights to be norm limits of complex symmetric operators. In particular, we prove a conjecture of Garcia and Poore. On the other hand, it is proved that an essentially normal operator is a norm limit of complex symmetric operators if and only if it is complex symmetric. We obtain a canonical decomposition for essentially normal operators which are complex symmetric. [ABSTRACT FROM AUTHOR]

In this paper we study the relations between the properties of the topological semigroup of all continuous selfmaps S(X) on a compact metric space X (the topological group H(X) of all homeomorphisms on X) and possible values of the topological entropy of its elements. In particular, we prove that topological entropy of a functional envelope on the space of all continuous selfmaps on Peano continua or on compact metric spaces with continuum many connected components has only two possible values 0 and +∞. [ABSTRACT FROM AUTHOR]

Several questions in complex analysis lead naturally to the study of bihomogeneous polynomials r(z,***) on Ćn X Ćn for which r(z,***) ||z||2d = ||h(z)||² for some natural number d and a holomorphic polynomial mapping h = (h1,...,hK) from Ćn to ĆK. When r has this property for some d, one seeks relationships between d, K, and the signature and rank of the coefficient matrix of r. In this paper, we reformulate this basic question as a question about the growth of the Hilbert function of a homogeneous ideal in Ć[z1,...,zn] and apply a well-known result of Macaulay to estimate some natural quantities. [ABSTRACT FROM AUTHOR]

In this paper we classify the maximal subsemigroups of the full transformation semigroup ΩΩ, which consists of all mappings on the infinite set Ω, containing certain subgroups of the symmetric group Sym(Ω) on Ω. In 1965 Gavrilov showed that there are five maximal subsemigroups of ΩΩ containing Sym(Ω) when Ω is countable, and in 2005 Pinsker extended Gavrilov's result to sets of arbitrary cardinality. We classify the maximal subsemigroups of ΩΩ on a set Ω of arbitrary infinite cardinality containing one of the following subgroups of Sym(Ω): the pointwise stabiliser of a non-empty finite subset of Ω, the stabiliser of an ultrafilter on Ω, or the stabiliser of a partition of Ω into finitely many subsets of eΩual cardinality. If G is any of these subgroups, then we deduce a characterisation of the mappings f,g ∈ ΩΩ such that the semigroup generated by G ∪ {f,g} eΩuals ΩΩ. [ABSTRACT FROM AUTHOR]

A deep result of J. Lewis (1983) shows that the polylogarithms Liɑ(z):= σk=1∞ zk/kɑ map the open unit disk D centered at the origin one-to-one onto convex domains for all ɑ ≥ 0. In the present paper this result is generalized to the so-called universal convexity and universal starlikeness (with respect to the origin) in the slit-domain &Lgr;:= C\[1, ∞), introduced by S. Ruscheweyh, L. Salinas and T. Sugawa (2009). This settles a conjecture made in that work and proves, in particular, that Liɑ(z) maps an arbitrary open disk or half-plane in &Lgr; one-to-one onto a convex domain for every ɑ ≥ 1. [ABSTRACT FROM AUTHOR]

We propose an approach to the attractors of skew products that tries to avoid unnecessary structures on the base space and rejects the assump-tion on the invariance of an attractor. When nonivertible maps in the base are allowed, one can encounter the mystery of the vanishing attractor. In the second part of the paper, we show that if the fiber maps are concave interval maps, then contraction in the fibers does not depend on the map in the base. [ABSTRACT FROM AUTHOR]

Let k be an algebraically closed field of characteristic p ≥ 0. Let A be a commutative k-algebra with multiplicative identity and let M be an A-module. Let G be a linear algebraic group acting rationally on both A and M. In this paper we study AG-modules of rath order invariants, In(M,G). The In(M,G) are defined inductively by I0(M, G) = {0} and In(M,G) = {m ∈ M:g.m --m ∈ In-1(M, G) for all g ∈ G}. We show that some fundamental problems concerning these modules can be reduced to the case In (k[G], G) where G acts on itself by right translation. We study the questions as to when In(M, G) is a finitely generated AG-module and how the In(M, G) are related to equivariant mappings. For the classical case of Ga acting on binary forms, we describe the In(M, G) and determine when they are Cohen-Macaulay. [ABSTRACT FROM AUTHOR]

Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations. [ABSTRACT FROM AUTHOR]

In the present paper, we prove the following result generalizing some well-known related results about biholomorphic or proper holomorphic mappings between some special domains in Cn. Let G1 and G2 be two compact Lie groups, which act linearly on Cn with O(Cn)Gj = C for j = 1, 2. Let 0 ∊ Ωj be bounded Gj -invariant domains in Cn for j = 1, 2. If f : Ω1 → Ω2 is a proper holomorphic mapping, then f extends holomorphically to an open neighborhood of Ω1, and in addition if f-1(0) = {0}, then f is a polynomial mapping. We also prove that if 0 ∊ Ω is a G1-invariant pseudoconvex domain in Cn with O(Cn)G1 = C, then Ω is orbit convex. The second result is used to prove the first one. [ABSTRACT FROM AUTHOR]

Let f : (C2, 0) → (C2, 0) be a germ of holomorphic skew product with a superattracting fixed point at the origin. If it has a suitable weight, then we can construct a Böttcher coordinate which conjugates f to the associated monomial map. This Böttcher coordinate is defined on an invariant open set whose interior or boundary contains the origin. [ABSTRACT FROM AUTHOR]

In this article, we establish some new second main theorems for meromorphic mappings of Cm into Pn(C) and moving hyperplanes with truncated counting functions. Our results are improvements of the previous second main theorems for moving hyperplanes with truncated (to level n) counting functions. [ABSTRACT FROM AUTHOR]

For any perfect fibration E → B, there is a “free loop transfer map” LB+ → LE+, defined using topological Hochschild homology. We prove that this transfer is compatible with the Becker-Gottlieb transfer, allowing us to extend a result of Dorabiała and Johnson on the transfer map in Waldhausen’s A-theory. In the case where E → B is a smooth fiber bundle, we also give a concrete geometric model for the free loop transfer in terms of Pontryagin-Thom collapse maps. We recover the previously known computations of the free loop transfer due to Schlichtkrull and make a few new computations as well. [ABSTRACT FROM AUTHOR]

A 3-manifold which admits a genus-2 reducible Heegaard splitting is one of the 3-sphere, 𝕊² × 𝕊¹, lens spaces and their connected sums. For each of those manifolds except most lens spaces, the mapping class group of the genus-2 splitting was shown to be finitely presented. In this work, we study the remaining generic lens spaces and show that the mapping class group of the genus-2 Heegaard splitting is finitely presented for any lens space by giving its explicit presentation. As an application, we show that the fundamental groups of the spaces of the genus-2 Heegaard splittings of lens spaces are all finitely presented. [ABSTRACT FROM AUTHOR]

Let SVdn be the Segre-Veronese variety given as the image of ℙn1 × ··· × ℙnr under the embedding induced by the complete linear system |Oℙn1 × ··· × ℙnr (d1,...,dr) |. We prove that asymptotically SVdn is not h-defective for h ≤ (min{ni})⎣log2(d-1)⎦, where d = d1 + ··· + dr. [ABSTRACT FROM AUTHOR]

We prove that the standard half-harmonic map U : R → S¹ defined by x → (x²-1/x²+1-2x/x²+1) is nondegenerate in the sense that all bounded solutions of the linearized halfharmonic map equation are linear combinations of three functions corresponding to rigid motions (dilation, translation, and rotation) of U. [ABSTRACT FROM AUTHOR]

The ray graph is a Gromov-hyperbolic graph on which the mapping class group of the plane minus a Cantor set acts by isometries. We give a description of the Gromov boundary of the ray graph in terms of cliques of long rays on the plane minus a Cantor set. As a consequence, we prove that the Gromov boundary of the ray graph is homeomorphic to a quotient of a subset of the circle. [ABSTRACT FROM AUTHOR]

We establish a modulus inequality, with weak assumptions on the Sobolev regularity, for homeomorphisms with integrable distortion. As an application, we find upper bounds for the pointwise rotation of planar homeomorphisms with p-integrable distortion. When the mapping is entire we bound the local pointwise rotation and when the mapping is restricted to a bounded convex domain Ω ⊂ C we concentrate on the rotation along the boundary. Furthermore, we show that these bounds are sharp in a very strong sense. Our examples will also prove that the modulus of continuity result, due to Koskela and Takkinen, for the homeomorphisms with p-integrable distortion is sharp in this strong sense. [ABSTRACT FROM AUTHOR]

Let E be a Bedford-McMullen carpet determined by a set of affine mappings (fij)(i,j)∈G and μ a self-affine measure on E associated with a probability vector (pij)(i,j)∈G. We prove that, for every r ∈ (0, ∞), the upper and lower quantization coefficient are always positive and finite in its exact quantization dimension sr. As a consequence, the nth quantization error for μ of order r is of the same order as n-1/sr. In sharp contrast to the Hausdorff measure for Bedford-McMullen carpets, our result is independent of the horizontal fibres of the carpets. [ABSTRACT FROM AUTHOR]

We give a complete characterization of Hamiltonian actions of compact Lie groups on exact symplectic manifolds with proper momentum maps. We deduce that every Hamiltonian action of a compact Lie group on a contractible symplectic manifold with a proper momentum map is globally linearizable. [ABSTRACT FROM AUTHOR]

We prove smooth and analytic versions of the classical Schwarz reflection principle for transversal CR mappings between two Levi-nondegenerate CR manifolds of hypersurface type. [ABSTRACT FROM AUTHOR]

To every singular reduced projective curve X one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compactification of a disjoint union of a finite number of copies of the generalized Jacobian of X. We investigate the geometric properties of fine compactified Jacobians focusing on curves having locally planar singularities. We give examples of nodal curves admitting nonisomorphic (and even nonhomeomorphic over the field of complex numbers) fine compactified Jacobians. We study universal fine compactified Jacobians, which are relative fine compactified Jacobians over the semiuniversal deformation space of the curve X. Finally, we investigate the existence of twisted Abel maps with values in suitable fine compactified Jacobians. [ABSTRACT FROM AUTHOR]

We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map. [ABSTRACT FROM AUTHOR]

Let X and Y be complex Banach spaces and denote by L(X) and L(Y) the algebras of all bounded linear operators on X, respectively Y. Let also x0 ∈ X and y0 ∈ Y be nonzero vectors. We prove that if ϕ : L(X)→L(Y) is a linear surjective map such that for each T ∈ L(X) we have that the local spectrum of ϕ(T) at y0 is a subset of the local spectrum of T at x0, then ϕ is automatically continuous. We also give a new proof for the automatic continuity of linear surjective maps decreasing the local spectral radius at some fixed nonzero vector. As a corollary, we obtain that the characterizations of J. Bračič and V. Müller for linear surjective maps on L(X) preserving the local spectrum/local spectral radius at some fixed vector can be obtained with no continuity assumptions on them. [ABSTRACT FROM AUTHOR]

Let D be the unit disc and z0 ϵ D. We determine the value range {f(z0) | f ϵ R≥}, where R≥ is the set of holomorphic functions f : D → D with f(0) = 0 and f'(0) ≥ 0 that have only real coefficients in their power series expansion around 0, and the smaller set {f(z0) | f ϵ R≥, f is typically real}. Furthermore, we describe a third value range {f(z0) | f ϵ I}, where I consists of all univalent self-mappings of the upper half-plane H with hydrodynamical normalization which are symmetric with respect to the imaginary axis. [ABSTRACT FROM AUTHOR]

We prove that the Weil-Petersson metric near the boundary of the Teichmüller space is C¹-asymptotically a product of the Weil-Petersson metric on a lower dimensional Teichmüller space and a metric on a model space. In particular, we show that theWeil-Petersson metric on the genus g, p-punctured Teichmüller space with 3g - 3 + p > 0 satisfies all the important properties required to apply the results in a previous work by the authors (2011). These estimates extend the well known C0 estimates for the Weil-Petersson metric. [ABSTRACT FROM AUTHOR]

We investigate the additivity A and lineability L cardinal coefficients for the following classes of functions: ES \ SES of everywhere surjective functions that are not strongly everywhere surjective, Darboux-like, Sierpiński-Zygmund, surjective, and their corresponding intersections. The classes SES and ES have been shown to be 2c-lineable. In contrast, although we prove here that ES \ SES is c+-lineable, it is still unclear whether it can be proved in ZFC that ES \ SES is 2c-lineable. Moreover, we prove that if c is a regular cardinal number, then A(ES \ SES) ≤ c. This shows that, for the class ES \ SES, there is an unusually large gap between the numbers A and L. [ABSTRACT FROM AUTHOR]

For d > 1, we consider the Veronese map of degree d on a complex vector space W, Verd : W → SymdW, w ↦ wd, and denote its image by Z. We describe the characters of the simple GL(W)-equivariant holonomic D-modules supported on Z. In the case when d = 2, we obtain a counterexample to a conjecture of Levasseur by exhibiting a GL(W)-equivariant D-module on the Capelli type representation Sym²W which contains no SL(W)-invariant sections. We also study the local cohomology modules H•Z(S), where S is the ring of polynomial functions on the vector space SymdW. We recover a result of Ogus showing that there is only one local cohomology module that is non-zero (namely in degree • = codim(Z)), and moreover we prove that it is a simple D-module and determine its character. [ABSTRACT FROM AUTHOR]