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- Title
A Note on Serrin's Type Problem on Riemannian Manifolds.
- Authors
Freitas, Allan; Roncoroni, Alberto; Santos, Márcio
- 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.
- Subjects
EINSTEIN, Albert, 1879-1955; SPACES of constant curvature; RIEMANNIAN manifolds; VECTOR fields
- Publication
Journal of Geometric Analysis, 2024, Vol 34, Issue 7, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-024-01650-5