Handbook of Hilbert geometry
by Papadopoulos, Athanase Troyanov, Marc
This volume presents surveys, written by experts in the field, on various classical and the modern aspects of Hilbert geometry. They are assuming several points of view: Finsler geometry, calculus of variations, projective geometry, dynamical systems, and others. Some fruitful relations between Hilbert geometry and other subjects in mathematics are emphasized, including Teichmüller spaces, convexity theory, Perron-Frobenius theory, representation theory, partial differential equations, coarse g…
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- Full title :Handbook of Hilbert geometry / Athanase Papadopoulos, Marc Troyanov, editors.
Summary
This volume presents surveys, written by experts in the field, on various classical and the modern aspects of Hilbert geometry. They are assuming several points of view: Finsler geometry, calculus of variations, projective geometry, dynamical systems, and others. Some fruitful relations between Hilbert geometry and other subjects in mathematics are emphasized, including Teichmüller spaces, convexity theory, Perron-Frobenius theory, representation theory, partial differential equations, coarse geometry, ergodic theory, algebraic groups, Coxeter groups, geometric group theory, Lie groups and discrete group actions. The Handbook is addressed to both students who want to learn the theory and researchers working in the area.
Read More ↓Edition Statements
- Publication Date:©2014
Publication Statements
- Publisher(s):European Mathematical Society
- Place of Publication:Zürich
- Language:eng
- Publication Date:©2014
Notes
MSC 53A35.
The Physical Object
- Description:VIII, 452 p. : : gráf. ; : 25 cm
Edition Identifiers
- ISBN:9783037191477, 3037191473
- oclc:on1322928639
- Dewey Decimal:516.9
Table of Contents
Weak Minkowski spaces / by Athanase Papadopoulos and Marc Troyanov -- From Funk to Hilbert geometry / by Athanase Papadopoulos and Marc Troyanov -- Funk and Hilbert geometries from the Finslerian viewpoint / by Marc Troyanov -- On the Hilbert geometry of convex polytopes / by Constantin Vernicos -- The horofunction boundary and isometry group of the Hilbert geometry / by Cormac Walsh -- Characterizations of hyperbolic geometry among Hilbert geometries / by Ren Guo -- The geodesic flow of Finsler and Hilbert geometries / by Mickaël Crampon -- Around groups in Hilbert geometry / by Ludovic Marquis -- Dynamics of Hilbert nonexpansive maps / by Anders Karlsson -- Birkhoff's version of Hilbert's metric and its applications in analysis / by Bas Lemmens and Roger Nussbaum -- Convex real projective structures and Hilbert metrics / by Inkang Kim and Athanase Papadopoulos -- Weil-Petersson Funk metric on Teichmüller space / by Hideki Miyachi, Ken'ichi Ohshika and Sumio Yamada -- Funk and Hilbert geometries in spaces of constant curvature / by Athanase Papadopoulos and Sumio Yamada -- On the origin of Hilbert geometry / by Marc Troyanov -- Hilbert's fourth problem / by Athanase Papadopoulos …
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