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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the Hilbert geometry of products
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by Constantin Vernicos PDF
Proc. Amer. Math. Soc. 143 (2015), 3111-3121 Request permission


We prove that the Hilbert geometry of a product of convex sets is bi-lipschitz equivalent to the direct product of their respective Hilbert geometries. We also prove that the volume entropy is additive with respect to product and that amenability of a product is equivalent to the amenability of each term.
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Additional Information
  • Constantin Vernicos
  • Affiliation: Institut de mathématique et de modélisation de Montpellier, Université Montpellier 2, Case Courrier 051, Place Eugène Bataillon, F–34395 Montpellier Cedex, France
  • Email:
  • Received by editor(s): January 30, 2012
  • Received by editor(s) in revised form: February 17, 2014
  • Published electronically: February 16, 2015
  • Communicated by: Michael Wolf
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3111-3121
  • MSC (2010): Primary 53C60; Secondary 53C24, 58B20, 53A20
  • DOI:
  • MathSciNet review: 3336635