曲率有界的Alexandrov曲面的正则性

Pub Date : 2016-11-10 DOI:10.1515/agms-2016-0012

L. Ambrosio, J. Bertrand

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引用次数: 12

摘要

摘要本文证明了在Alexandrov曲率有界的曲面上，距离来源于一个黎曼度规，对于任意p∈[1,2]，黎曼度规的分量局部属于离散奇异集中的W1,p。这个结果是基于Reshetnyak在更一般的曲面上的工作，这些曲面具有有界的积分曲率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Regularity of Alexandrov Surfaces with Curvature Bounded Below

Abstract In 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.

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