04273nam 22008775a 450 99101558277033212014-12-013-03719-647-510.4171/147(CKB)3710000000977188(CH-001817-3)184-141117(PPN)182624528(DE-4084)10.4171/147(EXLCZ)99371000000097718820141201j20141201 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierHandbook of Hilbert GeometryEMS Press20141 online resource (460 pages)IRMA Lectures in Mathematics and Theoretical Physics (irma)222523-5141Weak 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 D. Nussbaum --Convex real projective structures and Hilbert metrics /Inkang Kim, Athanase Papadopoulos --Weil-Petersson 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.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.Differential & Riemannian geometrybicsscDifferential geometrymscGeometrymscConvex and discrete geometrymscGlobal analysis, analysis on manifoldsmscDifferential & Riemannian geometryDifferential geometryGeometryConvex and discrete geometryGlobal analysis, analysis on manifolds01A55msc35Q53msc37D25msc37D20msc37D40msc47H09msc51-00msc51-02msc51-03msc51A05msc51B20msc51F99msc51K05msc51K10msc51K99msc51M10msc52A07msc52A20msc52A99msc53A20msc53A35msc53B40msc53C22msc53C24msc53C60msc53C70msc57S25msc58-00msc58-02msc58-03msc58B20msc58D05mscPapadopoulosedt2012174Papadopoulos AthanaseTroyanov MarcDE-4084BOOK9910155827703321Handbook of Hilbert Geometry4805606UNINA