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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 23656, 20 pages
http://dx.doi.org/10.1155/IJMMS/2006/23656

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 Hindawi Publishing Corporation. 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.

Linked References

  1. W. Ballmann, Lectures on Spaces of Nonpositive Curvature, vol. 25 of DMV Seminar, Birkhäuser, Basel, 1995, with an appendix by M. Brin: Ergodicity of Geodesic Flows. View at Zentralblatt MATH · View at MathSciNet
  2. W. Ballmann, M. Gromov, and V. Schroeder, Manifolds of Nonpositive Curvature, vol. 61 of Progress in Mathematics, Birkhäuser Boston, Massachusetts, 1985. View at Zentralblatt MATH · View at MathSciNet
  3. G. Beer, Topologies on Closed and Convex Sets, vol. 268 of Mathematics and Its Applications, Kluwer Academic, Dordrecht, 1993. View at Zentralblatt MATH · View at MathSciNet
  4. G. Birkhoff, “Extensions of Jentzsch's theorem,” Transactions of the American Mathematical Society, vol. 85, no. 1, pp. 219–227, 1957. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. Busemann, The Geometry of Geodesics, Academic Press, New York, 1955. View at Zentralblatt MATH · View at MathSciNet
  6. P. de la Harpe, “On Hilbert's metric for simplices,” in Geometric Group Theory, Vol. 1 (Sussex, 1991), London Mathematical Society Lecture Note Series, pp. 97–119, Cambridge University Press, Cambridge, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. T. Foertsch and A. Karlsson, “Hilbert metrics and Minkowski norms,” Journal of Geometry, vol. 83, no. 1-2, pp. 22–31, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. D. Hilbert, “Über die gerade Linie als kürzeste Verbindung zweier Punkte,” Mathematische Annalen, vol. 46, no. 1, pp. 91–96, 1895. View at Publisher · View at Google Scholar
  9. J.-B. Hiriat-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms I, vol. 305 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, 1993. View at Zentralblatt MATH · View at MathSciNet
  10. A. Karlsson, “Non-expanding maps and Busemann functions,” Ergodic Theory and Dynamical Systems, vol. 21, no. 5, pp. 1447–1457, 2001. View at Publisher · View at Google Scholar
  11. A. Karlsson and F. Ledrappier, “On laws of large numbers for random walks,” The Annals of Probability, vol. 34, no. 5, 2006. View at Publisher · View at Google Scholar
  12. A. Karlsson and G. A. Noskov, “The Hilbert metric and Gromov hyperbolicity,” L'Enseignement Mathématique. IIe Série, vol. 48, no. 1-2, pp. 73–89, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. E. Kohlberg and A. Neyman, “Asymptotic behavior of nonexpansive mappings in normed linear spaces,” Israel Journal of Mathematics, vol. 38, no. 4, pp. 269–275, 1981. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. E. Kohlberg and J. W. Pratt, “The contraction mapping approach to the Perron-Frobenius theory: why Hilbert's metric?” Mathematics of Operations Research, vol. 7, no. 2, pp. 198–210, 1982. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. V. Metz, “The short-cut test,” Journal of Functional Analysis, vol. 220, no. 1, pp. 118–156, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. R. D. Nussbaum, Hilbert's Projective Metric and Iterated Nonlinear Maps, vol. 75 of Memoirs of the American Mathematical Society, American Mathematical Society, Rhode Island, 1988. View at Zentralblatt MATH · View at MathSciNet
  17. M. A. Rieffel, “Group C-algebras as compact quantum metric spaces,” Documenta Mathematica, vol. 7, pp. 605–651, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet