黎曼流形上变分避障的局部极小化

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-12 DOI:10.3934/jgm.2023003

Jacob R. Goodman

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引用次数: 11

摘要

研究了完全黎曼流形上的变分避障问题。也就是说，我们在一组可容许曲线中最小化一个动作函数，这取决于用于避开障碍物的人工势函数。特别地，我们推广了双雅可比域和双共轭点的理论，并给出了最优性的充分必要条件。动作泛函的局部最小值被分为两类-称为$ Q $-局部最小值和$ \Omega $-局部最小值-随后进行分类，并在这两种情况下获得局部唯一性结果。

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Local minimizers for variational obstacle avoidance on Riemannian manifolds

This paper studies a variational obstacle avoidance problem on complete Riemannian manifolds. That is, we minimize an action functional, among a set of admissible curves, which depends on an artificial potential function used to avoid obstacles. In particular, we generalize the theory of bi-Jacobi fields and biconjugate points and present necessary and sufficient conditions for optimality. Local minimizers of the action functional are divided into two categories—called $ Q $-local minimizers and $ \Omega $-local minimizers—and subsequently classified, with local uniqueness results obtained in both cases.

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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.