Fridman’s Invariant, Squeezing Functions, and Exhausting Domains

Abstract

We show that if a bounded domain Ω is exhausted by a bounded strictly pseudoconvex domain D with C 2 boundary, then Ω is holomorphically equivalent to D or the unit ball, and show that a bounded domain has to be holomorphically equivalent to the unit ball if its Fridman's invariant has certain growth condition near the boundary.

Squeezing Function on Infinitely Connected Planar Domain

“…A domain is said to be holomorphic homogenous regular(HHR) domain if squeezing function on it admits positive lower bounds. For other important properties of squeezing functions one can refer the following papers: [3], [9], [13], [14], [16], [17], [18] and references therein.…”

On the generalized squeezing functions and Fridman invariants of special domains

“…There have also been some studies on ẽD and e D (see e.g. [6,10,18,20]). For more details on various recent results, we refer the readers to the survey papers [7,25].…”

Favouring a Dignified End to Human Life: Common Cause v. Union of India

“…A domain is said to be a holomorphic homogeneous regular (HHR) domain if the squeezing function on it admits a positive lower bound. For other important properties of squeezing functions, see, for example: [4,13,17,18,[21][22][23] and references therein.…”