Calculus of Variations and Geometric Measure Theory

G. De Philippis - M. Marini - E. Mukoseeva

The sharp quantitative isocapacitary inequality

created by dephilipp on 31 Jan 2019
modified on 01 Feb 2019


Submitted Paper

Inserted: 31 jan 2019
Last Updated: 1 feb 2019

Year: 2019

ArXiv: 1901.11309 PDF


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).