The Riemannian structure of Alexandrov spaces

Yukio Otsu, Takashi Shioya

Research output: Contribution to journalArticlepeer-review

117 Citations (Scopus)


Let X be an n -dimensional Alexandrov space of curvature bounded from below. We define the notion of singular point in X, and prove that the set Sχ of singular points in X is of Hausdorff dimension ≤ n - 1 and that X - Sx has a natural C°-Riemannian structure.

Original languageEnglish
Pages (from-to)629-658
Number of pages30
JournalJournal of Differential Geometry
Issue number3
Publication statusPublished - May 1994

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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