A free boundary problem associated with the isoperimetric inequality
Complex Variables
2024-05-14 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
This paper proves a 30 year old conjecture that disks and annuli are the only domains where analytic content - the uniform distance from 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.
Cite
@article{arxiv.1601.03885,
title = {A free boundary problem associated with the isoperimetric inequality},
author = {Ar. Abanov and C. Beneteau and D. Khavinson and R. Teodorescu},
journal= {arXiv preprint arXiv:1601.03885},
year = {2024}
}