Finite Type Conditions on Reinhardt Domains

TL;DR

This paper proves that for smoothly bounded pseudoconvex Reinhardt domains, the variety type at boundary points matches the regular type, simplifying the understanding of boundary geometry.

Contribution

It establishes the equality of variety type and regular type at boundary points of Reinhardt domains, providing new insights into their geometric structure.

Findings

Variety type equals regular type at boundary points

Simplifies boundary geometry analysis of Reinhardt domains

Enhances understanding of pseudoconvex domain properties

Abstract

In this paper we prove that, if $p$ is a boundary point of a smoothly bounded pseudoconvex Reinhardt domain in $\C^n$, then the variety type at $p$ is identical to the regular type.