The sharp quantitative isocapacitary inequality

2019/01/31 by De Philippis, Guido, Marini, Michele, Mukoseeva, Ekaterina
#49R05 (47A75 49Q20) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.11309

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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