Yuanpu Xiong

activity

20192026

collaborators

14 papers

math.DG2026

Scalar Curvature, Volumes and the Bergman Kernel

Bo-Yong Chen, Yuanpu Xiong, Liyou Zhang

Motivated by the works of Gromov and LeBrun in Riemannian geometry, we study the analogous phenomena in complex geometry. We first show that both $\int_{M} ∣ S_{C}^{-} (g) ∣^{n} d V_{g}$ and ${\r…

math.CV2025

The Grothendieck Theorem in Bergman Spaces

Yutao Liu, Jujie Wu, Yuanpu Xiong

In this paper, we prove that if $E$ is a closed subspace of the holomorphic $L^{p}$ -integrable space and is also contained in the holomorphic $L^{q}$ -integrable space, for any $p > 1$ …

math.CV2025

An estimate of the Bergman distance on Riemann surfaces

Bo-Yong Chen, Yuanpu Xiong

Let $M$ be a hyperbolic Riemann surface with the first eigenvalue $λ_{1} (M) > 0$ . Let $ρ$ denote the distance from a fixed point $x_{0} \in M$ and $r_{x}$ the injectivity radius at $x$ . We…

math.CV2024

Real Variable Things in Bergman Theory

Bo-Yong Chen, Yuanpu Xiong

In this article, we investigate the connection between certain real variable things and the Bergman theory. We first use Hardy-type inequalities to give an $L^{2}$ Hartogs-type exten…

math.CV2024

Convexity of the Bergman Kernels on Convex Domains

Yuanpu Xiong

Let $Ω$ be a convex domain in $C^{n}$ and $φ$ a convex function on $Ω$ . We prove that $lo g K_{Ω, φ} (z)$ is a convex function (might be identically $- \infty$ ) on $Ω$ , where…

math.DG2024

Type problem, the first eigenvalue and Hardy inequalities

Gilles Carron, Bo-Yong Chen, Yuanpu Xiong

In this paper, we study the relationship between the type problem and the asymptotic behaviour of the first (Dirichlet) eigenvalues $λ_{1} (B_{r})$ of ``balls'' $B_{r} := {ρ < r}$ on a comp…

math.DG2024

Type problem and the first eigenvalue

Bo-Yong Chen, Yuanpu Xiong

In this paper, we study the relationship between the type problem and the asymptotic behavior of the first eigenvalues $λ_{1} (B_{r})$ of ``balls'' $B_{r} := {ρ < r}$ on a complete Riemanni…

math.CV2023

Minimal $L^{2}$ and $L^{p}$ Ohsawa-Takegoshi extensions

Yuanpu Xiong

We find a precise relationship between the minimal extensions in $L^{2}$ and $L^{p}$ Ohsawa-Takegoshi extension theorems. This relationship also gives another proof to the $L^{p}$ versio…

math.CV2023

Equality between the Bergman metric and Carathéodory metric

Bo-Yong Chen, Yuanpu Xiong, Liyou Zhang

We present an equality between the Bergman metric and Carathéodry metric.

math.CV2023

Bergman functions on weakly uniformly perfect domains

Yuanpu Xiong, Zhiyuan Zheng

We contruct two classes of Zalcman-type domains, on which the Bergman distance functions have certain pre-described boundary behaviors. Such examples also lead to generalizations o…

math.CV2023

Regularity of the $p -$ Bergman kernel

Bo-Yong Chen, Yuanpu Xiong

We show that the $p -$ Bergman kernel $K_{p} (z)$ on a bounded domain $Ω$ is of locally $C^{1, 1}$ for $p \geq 1$ .The proof is based on the locally Lipschitz continuity of the off-diagonal…

math.CV2022

Some properties of the $p -$ Bergman kernel and metric

Bo-Yong Chen, Yuanpu Xiong

The $p -$ Bergman kernel $K_{p} (\cdot)$ is shown to be of $C^{1, 1/2}$ for $1 < p < \infty$ . An unexpected relation between the off-diagonal $p -$ Bergman kernel $K_{p} (\cdot, z)$ and certain we…

math.CV2021

A Psh Hopf Lemma for Domains with Cusp Conditions

Bo-Yong Chen, Yuanpu Xiong

We obtain a psh Hopf lemma for domains satisfying certain cusp conditions by using a sharp estimate for the Green function of a planar cusp along the axis. As an application, we ob…

math.CV2019

Curvature and $L^{p}$ Bergman spaces on complex submanifolds in $C^{N}$

Bo-Yong Chen, Yuanpu Xiong

Let $M$ be a closed complex submanifold in $C^{N}$ with the complete Kähler metric induced by the Euclidean metric. Several finiteness theorems on the $L^{p}$ Bergman space o…

Scalar Curvature, Volumes and the Bergman Kernel

The Grothendieck Theorem in Bergman Spaces

An estimate of the Bergman distance on Riemann surfaces

Real Variable Things in Bergman Theory

Convexity of the Bergman Kernels on Convex Domains

Type problem, the first eigenvalue and Hardy inequalities

Type problem and the first eigenvalue

Minimal L2 and Lp Ohsawa-Takegoshi extensions

Equality between the Bergman metric and Carathéodory metric

Bergman functions on weakly uniformly perfect domains

Regularity of the p−Bergman kernel

Some properties of the p−Bergman kernel and metric

A Psh Hopf Lemma for Domains with Cusp Conditions

Curvature and Lp Bergman spaces on complex submanifolds in CN

Minimal $L^{2}$ and $L^{p}$ Ohsawa-Takegoshi extensions

Regularity of the $p -$ Bergman kernel

Some properties of the $p -$ Bergman kernel and metric

Curvature and $L^{p}$ Bergman spaces on complex submanifolds in $C^{N}$