Analytic content and the isoperimetric inequality in higher dimensions
Classical Analysis and ODEs
2018-08-21 v3
Abstract
This paper establishes a conjecture of Gustafsson and Khavinson, which relates the analytic content of a smoothly bounded domain in to the classical isoperimetric inequality. The proof is based on a novel combination of partial balayage with optimal transport theory.
Keywords
Cite
@article{arxiv.1703.09922,
title = {Analytic content and the isoperimetric inequality in higher dimensions},
author = {Stephen J. Gardiner and Marius Ghergu and Tomas Sjödin},
journal= {arXiv preprint arXiv:1703.09922},
year = {2018}
}
Comments
15 pages (There was a gap in a proof in the first version. The main result is unchanged, but the proof has been corrected in the later versions.)