黎曼曲面近规则子集上弱测地线的局部最小性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-02 DOI:10.1007/s00009-024-02648-7

Juan Ferrera, Mohamad R. Pouryayevali, Hajar Radmanesh

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引用次数: 0

摘要

在本文中，我们证明了在黎曼流形的近规则子集中，每一条具有恒定速度的局部最小化曲线都是一条弱大地线。此外，本文还证明了在某些假设条件下，每条弱大地线都是局部最小化的。此外，还引入了近规则集上闭合弱大地线的概念，并将这些曲线表征为能量函数的非光滑临界点。

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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Local Minimality of Weak Geodesics on Prox-Regular Subsets of Riemannian Manifolds

In this paper, we prove that every locally minimizing curve with constant speed in a prox-regular subset of a Riemannian manifold is a weak geodesic. Moreover, it is shown that under certain assumptions, every weak geodesic is locally minimizing. Furthermore, a notion of closed weak geodesics on prox-regular sets is introduced and a characterization of these curves as nonsmooth critical points of the energy functional is presented.

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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.