A rigidity problem on the round sphere
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🧮 math.AP
math.DG
keywords
caseoverdeterminedproblemrigidityrotationallyroundspacessphere
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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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