强伪凸域中的Gehring-Hayman不等式

在$\mathbb{C}^2$中有限型伪凸域上的Gehring-Hayman型定理

The Gehring-Hayman type theorem on pseudoconvex domains of finite type in $\mathbb{C}^2$

本文在$\mathbb{C}^2$中有限型光滑有界伪凸域上证明了Gehring-Hayman型定理，并据此给出了边界点附近全局与局部Kobayashi距离的定量比较。

The Gehring-Hayman type theorems on complex domains

In this paper we establish Gehring-Hayman type theorems for some complex domains. Suppose that $Ω\subset \mathbb{C}^n$ is a bounded $m$-convex domain with Dini-smooth boundary, or a bounded strongly pseudoconvex domain with $C^2$-smooth boundary. Then we prove that the Euclidean length of Kobayashi geodesic $[x,y]$ in $Ω$ is less than $c_1|x-y|^{c_2}$. Furthermore, if $Ω$ endowed with the Kobayashi metric is Gromov hyperbolic, then we can generalize this result to quasi-geodesics with respect to Bergman metric, Carathéodory metric or Kähler-Einstein metric. As applications, we prove the bi-Höl…

关于单射亚纯映射的Gehring-Hayman不等式

Gehring-Hayman Inequality for Meromorphic Univalent Mappings

本文证明了亚纯单射函数的Gehring-Hayman不等式，并扩展了经典不等式到亚纯函数，同时验证了一个猜想。

Gromov 超几何性 I：关于准测地线的无维 Gehring-Hayman 不等式

The dimension-free Gehring-Hayman inequality for quasigeodesics

本文研究无限维空间中均匀性与 Gromov 超几何性关系，建立无维 Gehring-Hayman 不等式，放宽准测地线和等价条件，证明其在 Banach 空间中成立。

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

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-Hölder map between the Euclidean boundary and Gromov boundary. As an application, we show the bi-Hölder 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.

Pommerenke's theorem on Gromov hyperbolic domains

We establish a version of a classical theorem of Pommerenke, which is a diameter version of the Gehring-Hayman inequality on Gromov hyperbolic domains of $\mathbb{R}^n$. Two applications are given. Firstly, we generalize Ostrowski's Faltensatz to quasihyperbolic geodesics of Gromov hyperbolic domains. Secondly, we prove that unbounded uniform domains can be characterized in the terms of Gromov hyperbolicity and a naturally quasisymmetric correspondence on the boundary, where the Gromov boundary is equipped with a Hamenstädt metric (defined by using a Busemann function).