Bi-H\"{o}lder extensions of quasi-isometries on pseudoconvex domains of finite type in $\mathbb{C}^2$

TL;DR

This paper proves that the identity map on certain pseudoconvex domains in c2^2 extends to a bi-Hf6lder map between boundaries, and applies this to quasi-isometries and boundary regularity results.

Contribution

It establishes bi-Hf6lder boundary extensions for the identity and quasi-isometries on finite type pseudoconvex domains in c2^2, advancing boundary regularity understanding.

Findings

Identity map extends to bi-Hf6lder boundary map.

Quasi-isometries also admit bi-Hf6lder boundary extensions.

Provides refined index for Gehring-Hayman theorem on m-convex domains.

Abstract

In this paper, we prove that the identity map for the smoothly bounded pseudoconvex domain of finite type in $\mathbb{C}^2$ extends to a bi-H\"{o}lder map between the Euclidean boundary and Gromov boundary. As an application, we show the bi-H\"{o}lder boundary extensions for quasi-isometries between these domains. Moreover, we get a more accurate index of the Gehring-Hayman type theorem for the bounded $m$-convex domains with Dini-smooth boundary.