The local structure of length spaces with curvature bounded above

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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.

Original languageEnglish (US)
Pages (from-to)409-456
Number of pages48
JournalMathematische Zeitschrift
Volume231
Issue number3
DOIs
StatePublished - Jul 1999

ASJC Scopus subject areas

  • Mathematics(all)

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