Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-21 DOI:10.1016/j.aim.2024.109889

Stefano Nardulli , Reinaldo Resende

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引用次数: 0

Abstract

In the present work, we consider area minimizing currents in the general setting of arbitrary codimension and arbitrary boundary multiplicity. We study the boundary regularity of 2d area minimizing currents, beyond that, several results are stated in the more general context of $(C_{0}, α_{0}, r_{0})$ -almost area minimizing currents of arbitrary dimension m and arbitrary codimension taking the boundary with arbitrary multiplicity. Furthermore, we do not consider any type of convex barrier assumption on the boundary, in our main regularity result which states that the regular set, which includes one-sided and two-sided points, of any 2d area minimizing current T is an open dense set in the boundary.

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具有任意编码维数和乘数的二维面积最小电流边界正则集合的密度

在本研究中，我们考虑了在任意编维度和任意边界多重性的一般背景下的面积最小化电流。我们研究了 2d 面积最小化电流的边界正则性，除此之外，我们还在任意维数 m 和任意编码维数的 (C0,α0,r0) 近似面积最小化电流的更一般背景下，以任意乘数取边界，阐述了几个结果。此外，在我们的主要正则性结果中，我们不考虑边界上任何类型的凸障碍假设，即任何 2d 面积最小化电流 T 的正则集合（包括单边点和双边点）是边界上的开放致密集合。

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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.