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Serrin's type Problems in convex cones in Riemannian manifolds

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arxiv 2501.05551 v1 pith:7C6IRG54 submitted 2025-01-09 math.DG math.AP

Murilo Araújo , Allan Freitas , Márcio Santos , Joyce Sindeaux This is my paper
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keywords conesproblemresultconvexmanifoldsproductsriemannianrigidity
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In this work, we discuss several results concerning Serrin's problem in convex cones in Riemannian manifolds. First, we present a rigidity result for an overdetermined problem in a class of warped products with Ricci curvature bounded below. As a consequence, we obtain a rigidity result for Einstein warped products. Next, we derive a soap bubble result and a Heintze-Karcher inequality that characterize the intersection of geodesic balls with cones in these spaces. Finally, we analyze the analogous ovedetermined problem for the drift Laplacian, where the ambient space is a cone in the Euclidean space.

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  1. Overdetermined elliptic problems on model Riemannian manifolds

    math.AP 2025-05 reject novelty 6.0 of 10

    An annular sector-like domain admitting an overdetermined Helmholtz solution in a space form must be a spherical sector and the solution is radially symmetric.

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