Series 
IRMA lectures in mathematics and theoretical physics ; 22 

IRMA lectures in mathematics and theoretical physics ;
22.

Subject 
Hilbert, David, 18621943.


Geometry  Foundations.

Alt Name 
Papadopoulos, Athanase,


Troyanov, Marc,

Add Title 
Hilbert geometry 
Description 
1 online resource (viii, 452 pages) : illustrations (some color). 

polychrome rdacc 
Bibliography Note 
Includes bibliographical references and index. 
Contents 
Weak Minkowski spaces / Athanase Papadopoulos, Marc Troyanov  From Funk to Hilbert geometry / Athanase Papadopoulos, Marc Troyanov  Funk and Hilbert geometries from the Finslerian viewpoint / Marc Troyanov  On the Hilbert geometry of convex polytopes / Constantin Vernicos  The horofunction boundary and isometry group of the Hilbert geometry / Cormac Walsh  Characterizations of hyperbolic geometry among Hilbert geometries / Ren Guo  Around groups in Hilbert geometry / Ludovic Marquis  The geodesic flow of Finsler and Hilbert geometries / Mickaël Crampon  Dynamics of Hilbert nonexpansive maps / Anders Karlsson  Birkhoff's version of Hilbert's metric and its applications in analysis / Bas Lemmens, Roger Nussbaum  Convex real projective structures and Hilbert metrics / Inkang Kim, Athanase Papadopoulos  WeilPetersson Funk metric on Teichmüller space / Hideki Miyachi, Ken'ichi Ohshika, Sumio Yamada  Funk and Hilbert geometries in spaces of constant curvature / Athanase Papadopoulos, Sumio Yamada  On the origin of Hilbert geometry / Marc Troyanov  Hilbert's fourth problem / Athanase Papadopoulos  Open problems. 
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, PerronFrobenius 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. 
Note 
Online resource; title from PDF title page (European Mathematical Society, viewed November 18, 2014). 
ISBN 
9783037196472 (electronic bk.) 

3037196475 (electronic bk.) 

9783037191477 

3037191473 
OCLC # 
895821326 
