# The Riemannian structure of Alexandrov spaces

@article{Otsu1994TheRS, title={The Riemannian structure of Alexandrov spaces}, author={Yukio Otsu and Takashi Shioya}, journal={Journal of Differential Geometry}, year={1994}, volume={39}, pages={629-658} }

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.

## 197 Citations

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Denote by A(n) the family of isometry classes of compact n-dimensional Alexandrov spaces with curvature ≥-1, and λk(M) the kth eigenvalue of the Laplacian on M∈A(n). We prove the continuity of…

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