TY - JOUR

T1 - A note on the squeezing function

AU - Solynin, Alexander Y.U.

N1 - Publisher Copyright:
© 2021 American Mathematical Society. All rights reserved.

PY - 2021/11

Y1 - 2021/11

N2 - 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]).

AB - 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]).

KW - Circularly slit disk

KW - Doubly connected domain

KW - Jenkins's module problem

KW - Squeezing function

UR - http://www.scopus.com/inward/record.url?scp=85114777080&partnerID=8YFLogxK

U2 - 10.1090/proc/15588

DO - 10.1090/proc/15588

M3 - Article

AN - SCOPUS:85114777080

SN - 0002-9939

VL - 149

SP - 4743

EP - 4755

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -