On the uniform squeezing property of bounded convex domains in $\mathbb C^n$

Kang-Tae Kim and Liyou Zhang

Vol. 282 (2016), No. 2, 341–358

DOI: 10.2140/pjm.2016.282.341

Abstract

We prove that the bounded convex domains and the $C^2$-smoothly bounded strongly pseudoconvex domains in ${ℂ}^n$ admit the uniform squeezing property. Moreover, we prove by the scaling method that the squeezing function approaches $1$ near the strongly pseudoconvex boundary points.

Keywords

squeezing function, convex domains, scaling method

Mathematical Subject Classification 2010

Primary: 32F45

Secondary: 32A25

Milestones

Received: 8 October 2014

Revised: 13 October 2015

Accepted: 11 November 2015

Published: 3 March 2016