Existence of parabolic boundary points of certain domains in $\mathbb C^2$

TL;DR

This paper investigates the existence and nonexistence of parabolic boundary points in specific convex domains within complex two-dimensional space, highlighting conditions for their presence or absence.

Contribution

It establishes new results on when parabolic boundary points exist or do not exist in certain convex domains in ^2, advancing understanding of boundary behavior in complex analysis.

Findings

Existence of parabolic boundary points in certain convex domains.

Nonexistence of parabolic boundary points of infinite type in some domains.

Conditions characterizing the presence or absence of these points.

Abstract

In this paper, the existence of parabolic boundary points of certain convex domains in $\mathbb C^2$ is given. On the other hand, the nonexistence of parabolic boundary points of infinite type of certain domains in $\mathbb C^2$ is also shown.