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

IF 1.1 3区数学 Q1 MATHEMATICS

Mediterranean Journal of Mathematics Pub Date : 2024-05-02 DOI:10.1007/s00009-024-02648-7

Juan Ferrera, Mohamad R. Pouryayevali, Hajar Radmanesh

引用次数: 0

Abstract

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.

查看原文本刊更多论文

黎曼曲面近规则子集上弱测地线的局部最小性

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。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.