A note on the squeezing function

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Abstract

The squeezing problem on $\mathbb{C}$ can be stated as follows.<br>Suppose that $\Omega$ is a multiply connected domain in the unit<br>disk $\mathbb{D}$ containing the origin $z=0$. How far can the<br>boundary of $\Omega$ be pushed from the origin by an injective<br>holomorphic function $f:\Omega\to \mathbb{D}$ keeping the origin<br>fixed?<br><br>In this note, we discuss recent results on this problem obtained<br>by Ng, Tang and Tsai (Math. Anal. 2020) and by Gumenyuk and Roth<br>(arXiv:2011.13734, 2020) and also prove few new results using a<br>method suggested in one of our previous papers (Zapiski Nauchn.<br>Sem. POMI 1993).
Original languageEnglish
Pages (from-to)13
JournalProceedings of the American Mathematical Society.
StatePublished - May 1 2021

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