Mathematische Zeitschrift

, Volume 231, Issue 3, pp 409–456

The local structure of length spaces with curvature bounded above

  • Bruce Kleiner

DOI: 10.1007/PL00004738

Cite this article as:
Kleiner, B. Math Z (1999) 231: 409. doi:10.1007/PL00004738


We show that a number of different notions of dimension coincide for length spaces with curvature bounded above. We then apply this result, showing that if X is a locally compact CAT(0) space with cocompact isometry group, then the dimension of the Tits boundary and the asymptotic cone(s) of X are determined by the maximal dimension of a flat in X.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Bruce Kleiner
    • 1
  1. 1. Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA (e-mail: US