2021/03/16 by Gautam Bharali, Bharali, Gautam · 1 citation
Mathematics · #32F18 (Secondary) #32F45 #32T25 (Primary) 32A19 #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.2103.09227
openalex publication_date 2021/03/16 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We revisit the phenomenon where, for certain domains D, if the squeezing function sD extends continuously to a point p∈ ∂D with value 1, then ∂D is strongly pseudoconvex around p. In ℂ2, we present weaker conditions under which the latter conclusion is obtained. In another direction, we show that there are bounded domains D\Subset ℂn, n≥ 2, that admit large ∂D-open subsets \mathscrO⊂ ∂D such that sD→ 0 approaching any point in \mathscrO. This is impossible for planar domains. We pose a few questions related to these phenomena. But the core result of this paper identifies a new family of holomorphic homogeneous regular domains. We show via a family of examples how abundant domains satisfying the conditions of this result are.