A Metric Inequality for the Thompson and Hilbert Geometries

Cormac Walsh 1 Roger D. Nussbaum
1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : There are two natural metrics defined on an arbitrary convex cone: Thompson\'s part metric and Hilbert\'s projective metric. For both, we establish an inequality giving information about how far the metric is from being non-positively curved.
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Submitted on : Monday, October 3, 2005 - 9:39:20 PM
Last modification on : Thursday, December 6, 2018 - 11:56:03 PM

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Cormac Walsh, Roger D. Nussbaum. A Metric Inequality for the Thompson and Hilbert Geometries. Journal of Inequalities in Pure and Applied Mathematics, School of Communications and Informatics, 2004, 5, pp.53. ⟨hal-00009458⟩

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