We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin’s overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally symmetric spaces which imply a rigidity result in the case of the round sphere.
Ciraolo, G., Vezzoni, L. (2017). A rigidity problem on the round sphere. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 19(5) [http://dx.doi.org/10.1142/S0219199717500018].
A rigidity problem on the round sphere
CIRAOLO, Giulio;
2017-01-01
Abstract
We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin’s overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally symmetric spaces which imply a rigidity result in the case of the round sphere.
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