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- Title
A NOTE ON LOCAL MINIMIZERS OF ENERGY ON COMPLETE MANIFOLDS.
- Authors
BATISTA, MÁRCIO; SANTOS, JOSÉ I.
- Abstract
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.
- Subjects
RIEMANNIAN manifolds; ENERGY function; METRIC spaces; MATHEMATICS theorems; HYPOTHESIS
- Publication
Topological Methods in Nonlinear Analysis, 2022, Vol 60, Issue 2, p565
- ISSN
1230-3429
- Publication type
Article
- DOI
10.12775/TMNA.2022.013