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On the Hilbert geometry of products


Author: Constantin Vernicos
Journal: Proc. Amer. Math. Soc. 143 (2015), 3111-3121
MSC (2010): Primary 53C60; Secondary 53C24, 58B20, 53A20
DOI: https://doi.org/10.1090/S0002-9939-2015-12504-X
Published electronically: February 16, 2015
MathSciNet review: 3336635
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Abstract: 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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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: Constantin.Vernicos@um2.fr

DOI: https://doi.org/10.1090/S0002-9939-2015-12504-X
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
Article copyright: © Copyright 2015 American Mathematical Society