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A Serrin-type symmetry result on model manifolds: an extension of the Weinberger argument (1708.02032v2)
Published 7 Aug 2017 in math.AP and math.DG
Abstract: We consider the classical "Serrin symmetry result" for the overdetermined boundary value problem related to the equation $\Delta u=-1$ in a model manifold of non-negative Ricci curvature. Using an extension of the Weinberger classical argument we prove a Euclidean symmetry result under a suitable "compatibility" assumption between the solution and the geometry of the model.
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