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arXiv · 1802.03614

Rigidity of manifolds admitting stable solutions of an elliptic problem

Marcio Batista·Jose I. Santos
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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.

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Marcio Batista, Jose I. Santos. 2018-02-10. Rigidity of manifolds admitting stable solutions of an elliptic problem. https://arxiv.org/abs/1802.03614

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