The Riemannian structure of Alexandrov spaces

Yukio Otsu, Takashi Shioya

Research output: Contribution to journalArticle

89 Citations (Scopus)

Abstract

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
Volume39
Issue number3
DOIs
Publication statusPublished - Jan 1 1994

Fingerprint

Alexandrov Space
Singular Point
Hausdorff Dimension
n-dimensional
Curvature

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

The Riemannian structure of Alexandrov spaces. / Otsu, Yukio; Shioya, Takashi.

In: Journal of Differential Geometry, Vol. 39, No. 3, 01.01.1994, p. 629-658.

Research output: Contribution to journalArticle

Otsu, Yukio ; Shioya, Takashi. / The Riemannian structure of Alexandrov spaces. In: Journal of Differential Geometry. 1994 ; Vol. 39, No. 3. pp. 629-658.
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