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Handbook of Hilbert Geometry

Athanase Papadopoulos and Marc Troyanov, editors
Publisher: 
European Mathematical Society
Publication Date: 
2015
Number of Pages: 
460
Format: 
Hardcover
Series: 
IRMA Lectures in Mathematics and Theoretical Physics 22
Price: 
98.00
ISBN: 
9783037191477
Category: 
Handbook
We do not plan to review this book.
  • Introducton

Part I. Minkowski, Hilbert and Funk geometries

  • A. Papadopoulos and M. Troyanov -- Weak Minkowski spaces
  • A. Papadopoulos and M. Troyanov -- From Funk to Hilbert geometry
  • M. Troyanov -- Funk and Hilbert geometries from the Finslerian viewpoint
  • C. Vernicos -- On the Hilbert geometry of convex polytopes
  • C. Walsh -- The horofunction boundary and isometry group of the Hilbert geometry
  • R. Guo -- Characterizations of hyperbolic geometry among Hilbert geometries

Part II. Groups and dynamics in Hilbert geometry

  • M. Crampon -- The geodesic flow of Finsler and Hilbert geometries
  • L. Marquis -- Around groups in Hilbert geometry
  • A. Karlsson -- Dynamics of Hilbert nonexpansive maps
  • B. Lemmens and R. Nussbaum -- Birkhoff's version of Hilbert's metric and and its applications in analysis

Part III. Developments and applications

  • I. Kim and A. Papadopoulos -- Convex real projective structures and Hilbert metrics
  • H. Miyachi, K. Ohshika, and S. Yamada -- Weil-Petersson Funk metric on Teichmüller space
  • A. Papadopoulos and S. Yamada -- Funk and Hilbert geometries in spaces of constant curvature

Part IV. History of the subject

  • M. Troyanov -- On the origin of Hilbert geometry
  • A. Papadopoulos -- Hilbert's fourth problem
  • Open problems
  • List of contributors
  • Index

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