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Handbook of Hilbert Geometry
IRMA Lectures in Mathematics and Theoretical Physics Vol. 22

Handbook of Hilbert Geometry

Athanase Papadopoulos (Université de Strasbourg, France)
Marc Troyanov (École Polytechnique Fédérale de Lausanne, Switzerland)

ISBN print 978-3-03719-147-7, ISBN online 978-3-03719-647-2
DOI 10.4171/147
December 2014, 460 pages, hardcover, 17 x 24 cm.
78.00 Euro

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.

Keywords: Hilbert metric, Funk metric, non-symmetric metric, Finsler geometry, Minkowski space, Minkowski functional, convexity, Cayley-Klein-Beltrami model, projective manifold, projective volume, Busemann curvature, Busemann volume, horofunction, geodesic flow, Teichmüller space, Hilbert fourth problem, entropy, geodesic, Perron-Frobenius theory, geometric structure, holonomy homomorphism

Further Information

Zentralblatt Mathematik