Exposing points on the boundary of a strictly pseudoconvex or a locally convexifiable domain of finite 1-type

TL;DR

The paper demonstrates that for certain bounded domains in complex space with specific convexity and type properties, there exists a biholomorphic map that exposes boundary points as global extreme points of a given type.

Contribution

It establishes the existence of biholomorphic maps exposing boundary points of finite 1-type in locally convexifiable domains with Stein neighborhoods.

Findings

Existence of biholomorphic maps exposing boundary points.

Boundary points of finite 1-type can be globally exposed.

Applicable to domains with Stein neighborhood basis.

Abstract

We show that for any bounded domain $\Omega\subset\Cp ^n$ of 1-type $2k $ which is locally convexifiable at $p\in b\Omega$, having a Stein neighborhood basis, there is a biholomorphic map $f:\bar{\Omega}\rightarrow \Cp ^n $ such that $f(p)$ is a global extreme point of type $2k$ for $f{(\bar\Omega)}$.