Weak Finsler structures and the Funk weak metric
Weak Finsler structures and the Funk weak metric
复制标题
弱 Finsler 结构和 Funk 弱度量
DOI：
10.1017/s0305004109002461
复制
发表时间：
2008
影响因子：
0.8
通讯作者：
M. Troyanov
中科院分区：
文献类型：
--
作者：
A. Papadopoulos;M. Troyanov
本文讨论度量和芬斯勒结构的一般概念，我们称之为弱度量和弱芬斯勒结构。任何凸整环都带有一个标准的弱Finsler结构，我们称之为重言式弱Finsler结构。我们计算距离重言式弱芬斯勒结构的域，我们表明，这些都是由所谓的芬克弱度量。最后，我们讨论的测地线，度量球，凸性，和刚性的性能的Funk弱度量的文件。
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, of convexity, and of rigidity properties of the Funk weak metric.