The sharp quantitative isocapacitary inequality

Ekaterina Mukoseeva; Guido De Philippis; Michele Marini

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The sharp quantitative isocapacitary inequality

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arxiv 1901.11309 v1 pith:FSBVWOVI submitted 2019-01-31 math.AP

Guido De Philippis , Michele Marini , Ekaterina Mukoseeva This is my paper

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keywords inequalityisocapacitaryquantitativesharpanalyseanswerasymmetryball

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We prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same volume bounds the square of the Fraenkel asymmetry of the set. This provides a positive answer to a conjecture of Hall, Hayman, and Weitsman (J. d' Analyse Math. '91).

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