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On an isoperimetric inequality for capacity conjectured by Pólya and Szegő. (English) Zbl 1219.49034

Summary: We study a conjecture by Pólya and Szegö on the approximation of the electrostatic capacity of convex bodies in terms of their surface measure. We prove that a “local version” of this conjecture holds true and we give some results which bring further evidence to its global validity.

MSC:

49Q10 Optimization of shapes other than minimal surfaces
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
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