Families of exposing maps in strictly pseudoconvex domains

TL;DR

This paper proves that for a family of strictly pseudoconvex domains varying smoothly, there exists a corresponding family of exposing maps that continuously vary for all boundary points, aiding in complex analysis and geometric function theory.

Contribution

It establishes the existence of a continuously varying family of exposing maps for all boundary points across a smoothly varying family of strictly pseudoconvex domains.

Findings

Existence of a continuous family of exposing maps for boundary points.

Applicability to families of domains varying in C2 topology.

Advancement in understanding boundary behavior in complex domains.

Abstract

We prove that given a family of strictly pseudoconvex domains varying in C2 topology on domains, there exists a continuously varying family of exposing maps for all boundary points of all domains.