关于完全流形上能量的局部极小值的注记

IF 0.7 4区数学 Q2 MATHEMATICS

Topological Methods in Nonlinear Analysis Pub Date : 2022-12-10 DOI:10.12775/tmna.2022.013

M. Batista, José I. Santos

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引用次数: 1

摘要

在本文中，我们研究了完全黎曼流形的几何刚度，它允许能量泛函的局部极小值。更准确地说，假设存在一个非平凡的局部极小子，并且在适当的假设下，所考虑的黎曼流形必须是一个具有翘曲度量的乘积流形。其次，在类似的假设下，我们以与Cheeger-Gromoll分裂定理相同的方式推导了几何分裂，并且我们还得到了关于局部极小值的信息。

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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A note on local minimizers of energy on complete manifolds

In this paper, we study the geometric rigidity of complete Riemannian manifolds admitting local minimizers of energy functionals. More precisely, assuming the existence of a non-trivial local minimizer and under suitable assumptions, a Riemannian manifold under consideration must be a product manifold furnished with a warped metric. Secondly, under similar hypotheses, we deduce a geometrical splitting in the same fashion as in the Cheeger-Gromoll splitting theorem and we also get information about local minimizers.

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来源期刊

Topological Methods in Nonlinear Analysis 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.