Weak Finsler structures and the Funk weak metric

• Published in: Mathematical Proceedings of the Cambridge Philosophical Society
• Publication date: 2009

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.

Reference

• GR-TR-ARTICLE-2009-004
• doi:10.1017/S0305004109002461
• View record in Web of Science

Record created on 2009-07-08, modified on 2017-05-12