Hilbert metrics and Minkowski norms |
| |
Authors: | Thomas Foertsch Anders Karlsson |
| |
Affiliation: | 1. Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universit?t Bonn, Beringstrasse 1, 53115, Bonn, Germany 2. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden
|
| |
Abstract: | It is shown that the Hilbert geometry (D, hD) associated to a bounded convex domain is isometric to a normed vector space if and only if D is an open n-simplex. One further result on the asymptotic geometry of Hilbert’s metric is obtained with corollaries for the behavior of geodesics. Finally we prove that every geodesic ray in a Hilbert geometry converges to a point of the boundary. |
| |
Keywords: | Primary 51Kxx 53C60 |
本文献已被 SpringerLink 等数据库收录! |
|