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arXiv · 1601.03885

A free boundary problem associated with the isoperimetric inequality

Ar. Abanov·C. Beneteau·D. Khavinson·R. Teodorescu
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Abstract

This paper proves a 30 year old conjecture that disks and annuli are the only domains where analytic content - the uniform distance from $\bar{z}$ to analytic functions - achieves its lower bound. This problem is closely related to several well-known free boundary problems, in particular, Serrin's problem about laminar flow of incompressible viscous fluid for multiply-connected domains, and Garabedian's problem on the shape of electrified droplets. Some further ramifications and open questions, including extensions to higher dimensions, are also discussed.

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Ar. Abanov, C. Beneteau, D. Khavinson, R. Teodorescu. 2016-01-15. A free boundary problem associated with the isoperimetric inequality. https://doi.org/10.1007/s11854-022-0074-1

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