Remarks on Manifolds with Two-Sided Curvature Bounds

Author:

Kapovitch Vitali1,Lytchak Alexander2

Affiliation:

1. University of Toronto , Toronto , Canada

2. Mathematisches Institut , Universität Köln , Köln , Germany

Abstract

Abstract We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Reference39 articles.

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3. [3] S. Alexander, V. Kapovitch, and A. Petrunin, Alexandrov geometry, Preprint, https://arxiv.org/abs/1903.08539 (2019).

4. [4] P. Albano, On the cut locus of closed sets, Nonlinear Anal. 125 (2015), 398–405. MR 3373591

5. [5] B. Andrews, Notes on the isometric embedding problem and the Nash-Moser implicit function theorem, Surveys in analysis and operator theory (Canberra, 2001), Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 40, Austral. Nat. Univ., Canberra, 2002, pp. 157–208. MR 1953483

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