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This is a Quantitative Study study.

October 17, 2025Open Access

Serrin-type problem in divergence form on Riemannian manifolds

Puntos clave

Proving that equality leads to isometric domains resembles classic results in riemannian geometry, enhancing understanding.
The investigation employs integral identities and the P-function method, demonstrating their utility in geometric inequalities.
Exploring these problems under non-negative ricci curvature, we extend traditional symmetry concepts into broader geometric contexts.
The findings indicate significant implications for boundary value problems in geometrically complex environments like riemannian manifolds.

Resumen

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.

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