Explicit universal bounds for squeezing functions of ($\mathbb{C}$-)convex domains

Abstract

We prove two separate lower bounds -- one for nondegenerate convex domains and the other for nondegenerate $\mathbb{C}$-convex (but not necessarily convex) domains -- for the squeezing function that hold true for all domains in ${\mathbb{C}}^n$, for a fixed $n\ge 2$, of the stated class. We provide explicit expressions in terms of $n$ for these estimates.

8 pages; added new references, a discussion on pp. 7,8 on the strictness of the inequalities in Theorems 1.1 and 1.2, and a question (Question 4.2 on p. 8)