Bharali, G (2023) A new family of holomorphic homogeneous regular domains and some questions on the squeezing function. In: International Journal of Mathematics .
|
PDF
int_jou_mat_ope_acc_2023.pdf - Published Version Download (393kB) | Preview |
Abstract
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 ⊂ ℂn, n ≥ 2, that admit large ∂D-open subsets O ⊂ ∂D such that sD → 0 approaching any point in O. 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. © 2023 World Scientific Publishing Company.
| Item Type: | Journal Article |
|---|---|
| Publication: | International Journal of Mathematics |
| Publisher: | World Scientific |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Holomorphic homogeneous regular domains; squeezing function |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 14 Jun 2023 12:57 |
| Last Modified: | 14 Jun 2023 12:57 |
| URI: | https://eprints.iisc.ac.in/id/eprint/81914 |
Actions (login required)
 |
View Item |
