Finite type domains with hyperbolic orbit accumulation points

TL;DR

This paper classifies finite type domains with hyperbolic orbit accumulation points in a72, showing they are biholomorphic to specific ellipsoids, extending previous results to less regular boundaries.

Contribution

It proves that such domains are biholomorphic to ellipsoids under boundary regularity assumptions, generalizing earlier work that required real analytic boundaries.

Findings

Domains are biholomorphic to ellipsoids a72

Finite type domains with hyperbolic orbit accumulation points are pseudoconvex

Extension of classification results to less regular boundaries

Abstract

In this paper, finite type domains with hyperbolic orbit accumulation points are studied. We prove, in case of $\mathbb{C}^2$, it has to be a (global) pseudoconvex domain, after an assumption of boundary regularity. Moreover, one of the applications will realize the classification of domains within this class, precisely the domain is biholomorphic to one of the ellipsoids $\lbrace (z, w): | z|^{2m}+| w|^2<1, m\in\mathbb{Z}^+\rbrace$. This application generalizes \cite{BP98} in which the boundary is assumed to be real analytic for the case of hyperbolic orbit accumulation points.