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Main Authors: Batista, Márcio, Santos, Márcio, da Silva, Antônio, Sindeaux, Joyce
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2507.17838
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author Batista, Márcio
Santos, Márcio
da Silva, Antônio
Sindeaux, Joyce
author_facet Batista, Márcio
Santos, Márcio
da Silva, Antônio
Sindeaux, Joyce
contents In this paper, we investigate an overdetermined boundary value problem of divergence type on bounded domains in Riemannian manifolds with non-negative Ricci curvature. Using integral identities and the $P$-function method, we derive geometric inequalities and rigidity results. Under natural conditions on the nonlinearity, we prove that equality implies the domain is isometric to a Euclidean ball, thereby extending classical symmetry results to the Riemannian setting.
format Preprint
id arxiv_https___arxiv_org_abs_2507_17838
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Serrin-type problem in divergence form on Riemannian manifolds
Batista, Márcio
Santos, Márcio
da Silva, Antônio
Sindeaux, Joyce
Differential Geometry
In this paper, we investigate an overdetermined boundary value problem of divergence type on bounded domains in Riemannian manifolds with non-negative Ricci curvature. Using integral identities and the $P$-function method, we derive geometric inequalities and rigidity results. Under natural conditions on the nonlinearity, we prove that equality implies the domain is isometric to a Euclidean ball, thereby extending classical symmetry results to the Riemannian setting.
title Serrin-type problem in divergence form on Riemannian manifolds
topic Differential Geometry
url https://arxiv.org/abs/2507.17838