On the Regularity of Alexandrov Surfaces with Curvature Bounded Below-Reference-Cited by-同舟云学术

On the Regularity of Alexandrov Surfaces with Curvature Bounded Below

Published:2016-11-10 Issue:1 Volume:4 Page:
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:
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Author:

Ambrosio Luigi¹,Bertrand Jérôme²

Affiliation:

1. 1Scuola Normale Superiore, Piazza dei Cavalieri 7 56126 Pisa, Italy

2. 2Institut de Mathématiques de Toulouse, UMR CNRS 5219, Université Toulouse III, 31062 Toulouse cedex 9, France

Abstract

AbstractIn this note, we prove that on a surface with Alexandrov’s curvature bounded below, the distance derives from a Riemannian metric whose components, for any p ∈ [1, 2), locally belong to W1,p out of a discrete singular set. This result is based on Reshetnyak’s work on the more general class of surfaces with bounded integral curvature.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/agms-2016-0012/pdf

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