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 $n\geq 2$, of the stated class. We provide explicit expressions in terms of $n$ for these estimates.