Handbook of Hilbert Geometry [electronic resource] /
Athanase Papadopoulos, Marc Troyanov
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2014
- 1 online resource (460 pages)
- IRMA Lectures in Mathematics and Theoretical Physics (IRMA) 22 .
Weak Minkowski spaces / From Funk to Hilbert geometry / Funk and Hilbert geometries from the Finslerian viewpoint / On the Hilbert geometry of convex polytopes / The horofunction boundary and isometry group of the Hilbert geometry / Characterizations of hyperbolic geometry among Hilbert geometries / Around groups in Hilbert geometry / The geodesic flow of Finsler and Hilbert geometries / Dynamics of Hilbert nonexpansive maps / Birkhoff’s version of Hilbert’s metric and its applications in analysis / Convex real projective structures and Hilbert metrics / Weil–Petersson Funk metric on Teichmüller space / Funk and Hilbert geometries in spaces of constant curvature / On the origin of Hilbert geometry / Hilbert’s fourth problem / Open problems. Athanase Papadopoulos, Marc Troyanov -- Athanase Papadopoulos, Marc Troyanov -- Marc Troyanov -- Constantin Vernicos -- Cormac Walsh -- Ren Guo -- Ludovic Marquis -- Mickaël Crampon -- Anders Karlsson -- Bas Lemmens, Roger Nussbaum -- Inkang Kim, Athanase Papadopoulos -- Hideki Miyachi, Ken’ichi Ohshika, Sumio Yamada -- Athanase Papadopoulos, Sumio Yamada -- Marc Troyanov -- Athanase Papadopoulos --
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037196472
10.4171/147 doi
Differential & Riemannian geometry
Differential geometry
Geometry
Convex and discrete geometry
Global analysis, analysis on manifolds
Weak Minkowski spaces / From Funk to Hilbert geometry / Funk and Hilbert geometries from the Finslerian viewpoint / On the Hilbert geometry of convex polytopes / The horofunction boundary and isometry group of the Hilbert geometry / Characterizations of hyperbolic geometry among Hilbert geometries / Around groups in Hilbert geometry / The geodesic flow of Finsler and Hilbert geometries / Dynamics of Hilbert nonexpansive maps / Birkhoff’s version of Hilbert’s metric and its applications in analysis / Convex real projective structures and Hilbert metrics / Weil–Petersson Funk metric on Teichmüller space / Funk and Hilbert geometries in spaces of constant curvature / On the origin of Hilbert geometry / Hilbert’s fourth problem / Open problems. Athanase Papadopoulos, Marc Troyanov -- Athanase Papadopoulos, Marc Troyanov -- Marc Troyanov -- Constantin Vernicos -- Cormac Walsh -- Ren Guo -- Ludovic Marquis -- Mickaël Crampon -- Anders Karlsson -- Bas Lemmens, Roger Nussbaum -- Inkang Kim, Athanase Papadopoulos -- Hideki Miyachi, Ken’ichi Ohshika, Sumio Yamada -- Athanase Papadopoulos, Sumio Yamada -- Marc Troyanov -- Athanase Papadopoulos --
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037196472
10.4171/147 doi
Differential & Riemannian geometry
Differential geometry
Geometry
Convex and discrete geometry
Global analysis, analysis on manifolds