The Riemannian structure of Alexandrov spaces

Yukio Otsu; Takashi Shioya

doi:10.4310/jdg/1214455075

The Riemannian structure of Alexandrov spaces

Yukio Otsu, Takashi Shioya

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

116 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 S_χ of singular points in X is of Hausdorff dimension ≤ n - 1 and that X - S_x has a natural C°-Riemannian structure.

Original language	English
Pages (from-to)	629-658
Number of pages	30
Journal	Journal of Differential Geometry
Volume	39
Issue number	3
DOIs	https://doi.org/10.4310/jdg/1214455075
Publication status	Published - 1994 May

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title = "The Riemannian structure of Alexandrov spaces",

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.",

author = "Yukio Otsu and Takashi Shioya",

year = "1994",

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AU - Otsu, Yukio

AU - Shioya, Takashi

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AB - 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.

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JO - Journal of Differential Geometry

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The Riemannian structure of Alexandrov spaces

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