International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 23656, 20 pages
Horoballs in simplices and Minkowski spaces
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
Received 5 August 2005; Revised 23 July 2006; Accepted 25 July 2006
Copyright © 2006 A. Karlsson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.