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Start Over Descriptor "[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]" Journal annales academiae scientiarum fennicae mathematica
2 results on '"[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]"'

1. Convergence of some horocyclic deformations to the Gardiner-Masur boundary

Author

Vincent Alberge, Institut de Recherche Mathématique Avancée (IRMA), Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), and ANR-12-BS01-0009,Finsler,Géométrie de Finsler et applications(2012)

Subjects
Teichmüller space, Pure mathematics, Mathematics::Dynamical Systems, General Mathematics, Boundary (topology), Deformation (meteorology), 01 natural sciences, Mathematics - Geometric Topology, symbols.namesake, [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], FOS: Mathematics, Ergodic theory, Thurston asymmetric metric, Complex Variables (math.CV), 0101 mathematics, Mathematics, Mathematics - Complex Variables, Mathematics::Complex Variables, Teichmueller metric, Riemann surface, 010102 general mathematics, Geometric Topology (math.GT), [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], Teichmueller space, Gardiner-Masur boundary, Mathematics::Geometric Topology, Jordan curve theorem, Foliation, 30F60, 32G15, 30F45, 32F45, Horocycle, symbols, Teichmueller disc, Thurston boundary, Mathematics::Differential Geometry, Extremal length
Abstract

International audience; We introduce a deformation of Riemann surfaces and we are interested in the convergence of this deformation to a point of the Gardiner-masur boundary of Teichmueller space. This deformation, which we call the horocyclic deformation, is directed by a projective measured foliation and belongs to a certain horocycle in a Teichmueller disc. Using works of Marden and Masur and works of Miyachi, we show that the horocyclic deformation converges if its direction is given by a simple closed curve or a uniquely ergodic measured foliation.

Published
2016
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2. On length spectrum metrics and weak metrics on Teichmüller spaces of surfaces with boundary

Author

Athanase Papadopoulos, Lixin Liu, Weixu Su, Guillaume Théret, Department of Mathematics, Zhongshan University, Max-Planck-Institut für Mathematik (MPI), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), and Université Louis Pasteur - Strasbourg I-Centre National de la Recherche Scientifique (CNRS)

Subjects
Teichmüller space, Pure mathematics, General Mathematics, media_common.quotation_subject, Teichmüller, Boundary (topology), Type (model theory), 32G15, 30F30, 30F60, Mathematics - Geometric Topology, Simple (abstract algebra), [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT], FOS: Mathematics, Divergence (statistics), media_common, Mathematics, Spectrum (functional analysis), Thurston's asymmetric metric, Geometric Topology (math.GT), Surface (topology), Infinity, length spectrum weak metric, length spectrum metric
Abstract

We define and study natural metrics and weak metrics on the Teichmuller space of a surface of topologically finite type with boundary. These metrics and weak metrics are associated to the hyperbolic length spectrum of simple closed curves and of properly embedded arcs in the surface. We give a comparison between the defined metrics on regions of Teichmuller space which we call "0-relative �-thick parts, for � > 0 and "0 � � > 0. We compare the topologies defined by these metrics on Teichmuller space and we study divergence to infinity with respect to these various metrics.

Published
2010
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