Symmetry and rigidity results for Serrin's overdetermined type problems in weighted Riemannian manifolds

Laura Accornero; Giulio Ciraolo

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arXiv · 2604.00740

Symmetry and rigidity results for Serrin's overdetermined type problems in weighted Riemannian manifolds

Laura Accornero·Giulio Ciraolo

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Abstract

We study Serrin's overdetermined boundary value problems in bounded domains on weighted Riemannian manifolds. When the closure of the domain is compact, we establish a rigidity result that characterizes both the solution and the geometry of the ambient manifold. We further address the case of domains with non-compact closure for manifolds conformally equivalent to the Euclidean space, possibly degenerating or becoming singular at a point, where both the weight and the conformal factor are radial functions.

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Laura Accornero, Giulio Ciraolo. 2026-04-01. Symmetry and rigidity results for Serrin's overdetermined type problems in weighted Riemannian manifolds. https://arxiv.org/abs/2604.00740

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