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Register a new userSerrins type problems in warped product manifolds
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In this paper we consider Serrins overdetermined problems in warped product manifolds and we prove Serrins type rigidity results by using the P-function approach introduced by Weinberger.
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We consider overdetermined problems of Serrins type in convex cones for (possibly) degenerate operators in the Euclidean space as well as for a suitable generalization to space forms. We prove rigidity results by showing that the existence of a solution implies that the domain is a spherical sector.
Alexandrovs theorem asserts that spheres are the only closed embedded constant mean curvature hypersurfaces in space forms. In this paper, we consider Alexandrovs theorem in warped product manifolds and prove a rigidity result in the spirit of Alexandrovs theorem. Our approach generalizes the proofs of Reilly and Ros and, under more restrictive assumptions, it provides an alternative proof of a recent theorem of Brendle.
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