On the squeezing function for finitely connected planar domains
Abstract
In a recent paper, Ng, Tang and Tsai (Math. Ann. 2020) have found an explicit formula for the squeezing function of an annulus via the Loewner differential equation. Their result has led them to conjecture a corresponding formula for planar domains of any finite connectivity stating that the extremum in the squeezing function problem is achieved for a suitably chosen conformal mapping onto a circularly slit disk. In this paper we disprove this conjecture. We also give a conceptually simple potential-theoretic proof of the explicit formula for the squeezing function of an annulus which has the added advantage of identifying all extremal functions.
Cite
@article{arxiv.2011.13734,
title = {On the squeezing function for finitely connected planar domains},
author = {Pavel Gumenyuk and Oliver Roth},
journal= {arXiv preprint arXiv:2011.13734},
year = {2021}
}
Comments
Version 2: (1) a statement on the history of the notion of squeezing function has been corrected; (2) a new reference [5] (F. Deng: Levi's problem, convexity, and squeezing functions on bounded domains) has been added; (3) a small technical issue with numbering of equations has been resolved