Weak Finsler structures and the Funk weak metric

• Autores: Athanase Papadopoulos, Marc Troyanov
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 147, Nº 2, 2009, págs. 419-437
• Idioma: inglés
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• Resumen

  • 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, of convexity, and of rigidity properties of the Funk weak metric.