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arXiv · 1703.09922

Analytic content and the isoperimetric inequality in higher dimensions

Stephen J. Gardiner·Marius Ghergu·Tomas Sjödin
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Abstract

This paper establishes a conjecture of Gustafsson and Khavinson, which relates the analytic content of a smoothly bounded domain in $\mathbb{R}^{N}$ to the classical isoperimetric inequality. The proof is based on a novel combination of partial balayage with optimal transport theory.

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Stephen J. Gardiner, Marius Ghergu, Tomas Sjödin. 2017-03-29. Analytic content and the isoperimetric inequality in higher dimensions. https://doi.org/10.1016/j.jfa.2018.08.004

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