arXiv subjects

Xingsi Pu

Publications and source records attributed to Xingsi Pu.

5 recordsLinked to original sources

arXiv2026

Geometry of bounded generic domains with piecewise smooth boundary

In this paper, we study the geometry of bounded domains with piecewise smooth boundary. Specifically, we obtain the relationship between the squeezing function corresponding to polydisk and Levi flatness on bounded generic convex domains. As an application, we prove that a two dimensional bounded generic convex domain with piecewise $C^2$-smooth boundary that admits a finite volume quotient is biholomorphic to bidisk. Moreover, we show that any Teichm$\ddot{\operatorname{u}}$ller space $\mathcal{T}_g$ with $g\geq2$ can not be biholomorphic to a bounded generic domain with piecewise $C^2$-smooth boundary.

math.CV↗

arXiv2024

Asymptotic characterizations of strong pseudoconvexity on pseudoconvex domains of finite type in $\mathbb{C}^2$

In this paper, we provide some characterizations of strong pseudoconvexity by the boundary behavior of intrinsic invariants for smoothly bounded pseudoconvex domains of finite type in $\mathbb{C}^2$. As a consequence, if such domain is biholomorphically equivalent to a quotient of the unit ball, then it is strongly pseudoconvex.

math.CV↗

arXiv2023

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

In this paper, we obtain the Gehring-Hayman type theorem on smoothly bounded pseudoconvex domains of finite type in $\mathbb{C}^2$. As an application, we provide a quantitative comparison between global and local Kobayashi distances near a boundary point for these domains.

math.CV↗

arXiv2023

The Kobayashi metric and Gromov hyperbolicity on pseudoconvex domains of finite type in $\mathbb{C}^2$

In this paper, we obtain a more precise estimate of Catlin-type distance for smoothly bounded pseudoconvex domain of finite type in $\mathbb{C}^2$. As an application, we get an alternative proof of the Gromov hyperbolicity of this domain equipped with the Kobayashi distance.

math.CV↗

arXiv2023

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.

math.CV↗