Pinchuk scaling method on domains with non-compact automorphism groups

TL;DR

This paper characterizes weakly pseudoconvex finite type domains in complex space by analyzing automorphism orbit boundary behavior using the Pinchuk scaling method.

Contribution

It introduces a new application of the Pinchuk scaling method to characterize domain types based on automorphism orbit boundary behavior.

Findings

Characterization of weakly pseudoconvex finite type domains.

Application of the Pinchuk scaling method to boundary behavior analysis.

Insights into automorphism groups of complex domains.

Abstract

In this paper, we characterize weakly pseudoconvex domains of finite type in $\mathbb C^n$ in terms of the boundary behavior of automorphism orbits by using the scaling method.