International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 17, Article ID 23656, 20 pages
doi:10.1155/IJMMS/2006/23656
Horoballs in simplices and Minkowski spaces
A. Karlsson1
, V. Metz2
and G.A. Noskov3
1Department of Mathematics, Royal Institute of Technology, Stockholm 10044, Sweden
2Faculty of Mathematics, Bielefeld University, Bielefeld 33501, Germany
3Sobolev Institute of Mathematics, Pevtsova 13, Omsk 644099, Russia
Abstract
We obtain precise descriptions of all horoballs for Hilbert's geometry on simplices and for normed finite-dimensional vector spaces with norm given by some polyhedron. Certain geometrical consequences are deduced and several other applications are pointed out, which concern the dynamics of important classes of nonlinear self-maps of convex cones.