Rectifiability of the free boundary for varifolds

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.1512/iumj.2021.70.9401

L. De Masi

引用次数: 7

Abstract

Abstract. We establish a partial rectifiability result for the free boundary of a k-varifold V . Namely, we first refine a theorem of Grüter and Jost by showing that the first variation of a general varifold with free boundary is a Radon measure. Next we show that if the mean curvature H of V is in L for some p ∈ [1, k], then the set of points where the k-density of V does not exist or is infinite has Hausdorff dimension at most k − p. We use this result to prove, under suitable assumptions, that the part of the first variation of V with positive and finite (k− 1)-density is (k− 1)-rectifiable.

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变量自由边界的可整流性

摘要我们建立了k-变量V的自由边界的部分可整流性结果。即，我们首先通过证明具有自由边界的一般变分的第一个变分是Radon测度来改进gr特尔定理和约斯特定理。其次，我们证明了对于某些p∈[1,k]，如果V的平均曲率H在L中，那么V的k密度不存在或无限的点的集合具有最多k−p的Hausdorff维数。我们利用这一结果证明了在适当的假设下，V的第一个变化具有正的有限(k−1)密度的部分是(k−1)可校正的。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.