A NOTE ON LOCAL MINIMIZERS OF ENERGY ON COMPLETE MANIFOLDS

被引：0
|
作者：
Batista, Marcio [1 ]
Santos, Jose I. [2 ]
机构：
[1] Univ Fed Alagoas, CPMAT IM, BR-57072900 Maceio, AL, Brazil
[2] Inst Fed Alagoas, BR-57608180 Palmeiras Dos Indios, AL, Brazil
来源：
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2022年 / 60卷 / 02期
关键词：
Stability; minimizer; manifolds; DE-GIORGI; CONJECTURE; SURFACES; GEOMETRY;
D O I：
10.12775/TMNA.2022.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the geometric rigidity of complete Rie-mannian 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 simi-lar 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.
引用
收藏
页码：565 / 579
页数：15
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