In a recent paper, Ng, Tang and Tsai (Math Ann 380, 1741–1766, https://doi.org/10.1007/s00208-020-02046-w, 2021) 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.

On the squeezing function for finitely connected planar domains

Gumenyuk P.;
2021-01-01

Abstract

In a recent paper, Ng, Tang and Tsai (Math Ann 380, 1741–1766, https://doi.org/10.1007/s00208-020-02046-w, 2021) 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.
2021
conformal mapping
squeezing function
extremal problem
finitely connected domain
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1194496
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