A note on the squeezing function

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Abstract

The squeezing problem on C can be stated as follows. Suppose that Ω is a multiply connected domain in the unit disk D containing the origin z = 0. How far can the boundary of Ω be pushed from the origin by an injective holomorphic function f : Ω → D keeping the origin fixed? In this note, we discuss recent results on this problem obtained by Ng, Tang and Tsai [Math. Anal. 380 (2021), pp. 1741-1766] and by Gumenyuk and Roth (arXiv:2011.13734, 2020) and also prove few new results using a method suggested in one of our previous papers (see Solynin [Zap. Nauchn. Sem. S. Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 204 (1993), pp. 11, 93-114, 169]).

Original languageEnglish
Pages (from-to)4743-4755
Number of pages13
JournalProceedings of the American Mathematical Society
Volume149
Issue number11
DOIs
StatePublished - Nov 2021

Keywords

  • Circularly slit disk
  • Doubly connected domain
  • Jenkins's module problem
  • Squeezing function

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