The sharp quantitative isocapacitary inequality
Analysis of PDEs
2019-02-01 v1
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).
Cite
@article{arxiv.1901.11309,
title = {The sharp quantitative isocapacitary inequality},
author = {Guido De Philippis and Michele Marini and Ekaterina Mukoseeva},
journal= {arXiv preprint arXiv:1901.11309},
year = {2019}
}