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Abstract: In this paper we study the centered and non-centered Hardy–Littlewood maximal functions, M and , for a wide class of non-doubling measure μ defined on cusped manifolds. In particular, we give a class of manifolds with exponential volume growth on which M is of weak type and is bounded on for all . [Copyright &y& Elsevier]

Abstract: In this paper we prove that every entire curve in a smooth hypersurface of degree in must satisfy an algebraic differential equation of order 3. The logarithmic version of this result is given proving that every entire curve in the complement of a smooth surface of degree in must satisfy an algebraic differential equation of order 3. [Copyright &y& Elsevier]

Abstract: In this paper we will study some questions concerning solutions of Yamabe''s equation on an annulus of with different data on the boundary. The important problem: “what about the radial solution u satisfying () and ” is solved. [Copyright &y& Elsevier]

Abstract: Let T be a closed positive current of dimension p in and H an analytic subvariety of of dimension . We denote by the slice of T in H if it exists. We consider the functions on defined by and . The aim of this paper is to establish relationship between the growth of these functions. We prove results generalizing those of L. Gruman in [Séminaire Lelong–Skoda 1981–1983, Lecture Notes in Math., vol. 1028, Springer-Verlag, Berlin, 1983, pp. 125–162] and B. Molzan, B. Shiffman and N. Sibony in [Math. Ann. 257 (1981) 43]. [Copyright &y& Elsevier]

In this paper we study the equation of an anisotropic rotating fluid evolving in a three-dimensional torus. The anisotropy of the fluid concerns the vertical viscosity which can be considered to be null. We prove that the equation is well posed on arbitrarily long time intervals, if the Rossby number is small enough. We also prove that the “filtered” solutions converge to the solution of the limit system. Those results hold for all tori (without imposing the non-resonant condition on the domain), in a functional frame very close to the critical regularity level. When the initial data is of null horizontal average, in the case of non-resonant tori as well as for certain resonant tori, we obtain the global existence and uniqueness of the solution. [Copyright &y& Elsevier]

Let Ω⊂RN be an open set. We consider on Ω the competitors (U,K) for the reduced Mumford–Shah functional, that is to say the Mumford–Shah functional in which the L2-norm of U term is removed, where K is a closed subset of Ω and U is a function on Ω&z.drule;K with gradient in L2. The main result of this paper is the following: there exists a constant c for which, whenever (U,K) is a quasi-minimizer for the reduced Mumford–Shah functional and B(x,r) is a ball centered on K and contained in Ω with bounded radius, the HN−1-measure of K∩B(x,r) is bounded above by crN−1 and bounded below by c−1rN−1. [Copyright &y& Elsevier]

In this paper, we present and solve some very general new Pade´ approximant problems, whose solutions can be expressed with hypergeometric series. These series appear in the proofs of the irrationality of ζ(3), of infinitely many ζ(2n+1), and in essentially all results of this kind in the literature. We also prove two new Diophantine results with this method. [Copyright &y& Elsevier]

In this paper, we consider the Lp boundedness of the Riesz transforms on the cone C(N)=R+×N, where N is a complete noncompact Riemannian manifold whose Ricci curvature is bounded from below. [Copyright &y& Elsevier]

Let M be a CR manifold. The main results of this paper are the following:(A)When M is real analytic, a semi-global Hartogs extension phenomenon occurs for real analytic CR functions if and only if M is nowhere strictly pseudoconvex and dimRM⩾3.(B)When M is a standard manifold, the Hartogs–Bochner extension phenomenon occurs for non-CR-confined domains if and only if M is nowhere strictly pseudoconvex and dimCRM⩾2.(C)If M is a smooth submanifold of Cn foliated by complex curves, a semi-global Hartogs–Bochner extension phenomenon occurs for smooth non-CR-confined domains if and only if dimCRM⩾2.(D)If M is a real analytic nowhere strictly pseudoconvex manifold and if Ω is a sufficiently small domain in M, a hyperfunction which is real analytic in a neighborhood of bΩ and CR in a neighborhood of Ω is in fact real analytic on Ω. [Copyright &y& Elsevier]

In this paper, we study the monodromy of the ramified Cauchy problem for operators with multiple characteristics of constant multiplicity. More precisely, we give an estimation of the eigenvalues of the solution''s monodromy, first with the assumptions of the theorem of Hamada–Leray–Wagschal, then with the assumptions of the theorem of Leichtnam. [Copyright &y& Elsevier]