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Weak Finsler Structures and the Funk Metric

Abstract : We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we show that these are given by the so-called Funk weak metric. We conclude the paper with a discussion of geodesics, of metric balls and of convexity properties of the Funk weak metric.
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https://hal.archives-ouvertes.fr/hal-00276958
Contributor : Athanase Papadopoulos Connect in order to contact the contributor
Submitted on : Sunday, May 4, 2008 - 8:15:15 PM
Last modification on : Wednesday, September 14, 2022 - 5:58:26 PM
Long-term archiving on: : Friday, May 28, 2010 - 6:18:01 PM

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Athanase Papadopoulos, Marc Troyanov. Weak Finsler Structures and the Funk Metric. Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press (CUP), 2009, 147 (2), ⟨10.1017/S0305004109002461⟩. ⟨hal-00276958⟩

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