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arXiv · 2301.06411

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

Jinsong Liu·Xingsi Pu·Hongyu Wang
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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.

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Jinsong Liu, Xingsi Pu, Hongyu Wang. 2023-01-16. Bi-H\"{o}lder extensions of quasi-isometries on pseudoconvex domains of finite type in $\mathbb{C}^2$. https://arxiv.org/abs/2301.06411

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