The sharp quantitative isocapacitary inequality

Guido de Philippis; Michele Marini; Ekaterina Mukoseeva

doi:10.4171/rmi/1259

The sharp quantitative isocapacitary inequality

Guido de Philippis, Michele Marini, Ekaterina Mukoseeva

Mathematics

Research output: Contribution to journal › Article › peer-review

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. Analyse Math.'91).

Original language	English (US)
Pages (from-to)	2191-2228
Number of pages	38
Journal	Revista Matematica Iberoamericana
Volume	37
Issue number	6
DOIs	https://doi.org/10.4171/rmi/1259
State	Published - 2021

Keywords

Fraenkel asymmetry
Isocapacitary inequality
Stability estimates

ASJC Scopus subject areas

General Mathematics

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10.4171/rmi/1259

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AB - 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. Analyse Math.'91).

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KW - Isocapacitary inequality

KW - Stability estimates

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The sharp quantitative isocapacitary inequality

Abstract

Keywords

ASJC Scopus subject areas

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