TY - JOUR AU - Batista, Márcio AU - Santos, José I. PY - 2022/12/10 Y2 - 2024/03/28 TI - A note on local minimizers of energy on complete manifolds JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 60 IS - 2 SE - DO - 10.12775/TMNA.2022.013 UR - https://apcz.umk.pl/TMNA/article/view/41316 SP - 565 - 579 AB - 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 bea product manifold furnished with a warped metric.Secondly, under similar hypotheses, we deduce a geometrical splitting inthe same fashion as in the Cheeger-Gromoll splitting theorem and we also get information about local minimizers. ER -