Mathematische Zeitschrift

, Volume 231, Issue 3, pp 409–456 | Cite as

The local structure of length spaces with curvature bounded above

  • Bruce Kleiner

Abstract.

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.

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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: bkleiner@math.utah.edu) US

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