A note on Serrin's type problem on Riemannian manifolds

Abstract

In this paper, we deal with Serrin-type problems in Riemannian manifolds. First, we obtain a Heintze-Karcher inequality and a Soap Bubble result, with its respective rigidity, when the ambient space has a Ricci tensor bounded below. After, we approach a Serrin problem in bounded domains of manifolds endowed with a closed conformal vector field. Our primary tool, in this case, is a new Pohozaev identity, which depends on the scalar curvature of the manifold. Applications involve Einstein and constant scalar curvature spaces.

Theorems & Definitions (12)

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• proof : Proof of Theorem \ref{['teoA']}
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• proof : Proof of Theorem \ref{['teoB']}
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• proof : Proof of Theorem \ref{['teoC']}