Title: A note on Serrin’s type problem on Riemannian manifolds
Authors: Allan Freitas, Alberto Roncoroni and M\’arcio Santos
Categories: math.DG math.AP
Comments: Comments are welcome!
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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.
\\ ( https://arxiv.org/abs/2305.19772 , 15kb)
