2021/01/09 by Alexander Yu. Solynin, Solynin, Alexander Yu.
Mathematics · #30C35 #30C75 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2101.03361
openalex publication_date 2021/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The squeezing problem on ℂ can be stated as follows. Suppose that Ω is a multiply connected domain in the unit disk \mathbbD containing the origin z=0. How far can the boundary of Ω be pushed from the origin by an injective holomorphic function f:Ω→ \mathbbD keeping the origin fixed? In this note, we discuss recent results on this problem obtained by Ng, Tang and Tsai (Math. Anal. 2020) 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 (Zapiski Nauchn. Sem. POMI 1993).