Rigidity of manifolds admitting stable solutions of an elliptic problem
Differential Geometry
2018-02-13 v1 Analysis of PDEs
Abstract
In this paper, we study geometric rigidity of Riemannian manifolds admitting stable solutions of certain elliptic problems (stability in a variational sense), that is, under suitable hypotheses, we are able to characterize the Riemannian manifold which admits a stable solution. Furthermore, under the non-negativity of the weighted Ricci curvature, we deduce several data about the stable solution and a splitting result for the manifold.
Keywords
Cite
@article{arxiv.1802.03614,
title = {Rigidity of manifolds admitting stable solutions of an elliptic problem},
author = {Marcio Batista and Jose I. Santos},
journal= {arXiv preprint arXiv:1802.03614},
year = {2018}
}