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On the squeezing function for finitely connected planar domains

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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.

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Authors and Affiliations

  1. Department of Mathematics, Politecnico di Milano, via E. Bonardi 9, 20133, Milan, Italy

    Pavel Gumenyuk

  2. Department of Mathematics, University of Würzburg, Emil Fischer Strasse 40, 97074, Würzburg, Germany

    Oliver Roth

Authors
  1. Pavel Gumenyuk
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  2. Oliver Roth
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Correspondence to Pavel Gumenyuk.

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Communicated by Ngaiming Mok.

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Gumenyuk, P., Roth, O. On the squeezing function for finitely connected planar domains. Math. Ann. 384, 1–24 (2022). https://doi.org/10.1007/s00208-021-02296-2

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  • DOI: https://doi.org/10.1007/s00208-021-02296-2

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