A note on local minimizers of energy on complete manifolds
DOI:
https://doi.org/10.12775/TMNA.2022.013Keywords
Stability, minimizer, manifoldsAbstract
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.References
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