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Symmetry problems: 2. (English) Zbl 1169.53320

Summary: Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to \(c/|x|\) for all sufficiently large \(|x|\), where \(c>0\) is a constant, then the surface is a sphere.

MSC:

53B50 Applications of local differential geometry to the sciences
53B21 Methods of local Riemannian geometry
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
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