English

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 RN\mathbb{R}^{N} 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.)

R2 v1 2026-06-22T19:00:30.827Z