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arXiv · 1901.11309

The sharp quantitative isocapacitary inequality

Guido De Philippis·Michele Marini·Ekaterina Mukoseeva
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Abstract

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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Guido De Philippis, Michele Marini, Ekaterina Mukoseeva. 2019-01-31. The sharp quantitative isocapacitary inequality. https://arxiv.org/abs/1901.11309

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