On the uniform squeezing property of bounded convex domains in ℂn

Abstract

We prove that the bounded convex domains and the C 2 -smoothly bounded strongly pseudoconvex domains in ‫ރ‬ 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.

Infinite Dimensional Holomorphic Homogeneous Regular Domains

“…In particular, it has been shown in [24] that a holomorphic homogeneous regular bounded domain D in C n must be pseudoconvex and all strongly convex domains in C n are holomorphic homogeneous regular. Recently, it has been shown in [14] that all bounded convex domains in C n are holomorphic homogeneous regular. The squeezing function on a bounded homogeneous domain in C n is constant, by its holomorphic invariance, and has been computed explicitly for the four classical series of Cartan domains in [17].…”

Holomorphic motions and complex geometry

“…According to [8,Theorem 4.1] it holds lim z→p σ Ω (z) = 1, where σ Ω is the squeezing function of Ω (see Definition in [8]). This means that for every ν ≥ 1 there exists a biholomorphism ϕ ν from Ω to some strongly pseudoconvex domain Ω ν and there exists a sequence (r ν ) ν with lim ν→∞ r ν = 1 such that for every ν ≥ 1:…”

Linear invariants of complex manifolds and their plurisubharmonic variations

“…We have known many homogeneous regular domains, such as Teichmüller spaces of compact Riemann surfaces, bounded homogeneous domains, strongly pseudoconvex domains with C 2 boundary, bounded convex domains, and bounded complex convex domains(see [16], [20], [25], [31]).…”