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Rigidity of Hilbert metrics

Published online by Cambridge University Press:  17 April 2009

Bruno Colbois  and
Patrick Verovic
Bruno Colbois
Affiliation:
Université de Neuchâtel, Institut de mathématiques, Rue Émile Argand 13, CH-2007 NeuchâtelSwitzerland e-mail: [email protected]
Patrick Verovic
Affiliation:
Université de Savoie, Campus scientifique, Laboratoire de mathématiques, 73376 Le Bourget-du-Lac cedex, France e-mail: [email protected]
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Abstract

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We study the groups of isometries for Hilbert metrics on bounded open convex domains in ℝn and show that if  is such a set with a strictly convex boundary, the Hilbert geometry is asymptotically Riemannian at infinity. As a consequence of this result, we prove there are no Hausdorff quotients of  by isometry subgroups with finite volume except when ∂ is an ellipsoid.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 23 - 34
Copyright
Copyright © Australian Mathematical Society 2002

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