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

TL;DR

This paper establishes explicit universal lower bounds for the squeezing functions of convex and $ ext{C}$-convex domains in complex spaces, enhancing understanding of their geometric properties.

Contribution

It introduces new explicit lower bounds for squeezing functions applicable to all convex and $ ext{C}$-convex domains in $ ext{C}^n$, with formulas depending on the dimension.

Findings

Derived explicit lower bounds for convex domains

Extended bounds to $ ext{C}$-convex domains

Provided formulas depending on the dimension $n$

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.