Stability from rigidity via umbilicity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-27 DOI:10.1515/acv-2023-0119

Julian Scheuer

引用次数: 0

Abstract

We consider a range of geometric stability problems for hypersurfaces of spaceforms. One of the key results is an estimate relating the distance to a geodesic sphere of an embedded hypersurface with integral norms of the traceless Hessian operator of a level set function for the open set bounded by the hypersurface. As application, we give a unified treatment of many old and new stability problems arising in geometry and analysis. Those problems ask for spherical closeness of a hypersurface, given a geometric constraint. Examples include stability in Alexandroff’s soap bubble theorem in space forms, Serrin’s overdetermined problem, a Steklov problem involving the bi-Laplace operator and non-convex Alexandroff–Fenchel inequalities.

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通过脐带从刚性中获得稳定性

我们考虑了空间形式超曲面的一系列几何稳定性问题。其中一个关键结果是对嵌入超曲面的大地球面距离与超曲面所界开集的无迹水平集函数的无迹黑森算子的积分规范的估计。作为应用，我们对几何和分析中出现的许多新旧稳定性问题进行了统一处理。这些问题要求在给定几何约束的情况下，超曲面的球面闭合性。例如，空间形式中亚历山德罗夫肥皂泡定理的稳定性、塞林过确定性问题、涉及双拉普拉斯算子的斯特克洛夫问题以及非凸亚历山德罗夫-芬切尔不等式。

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.