Bo Chen

activity

20232026

collaborators

9 papers

math.CV2026

Quantitative hyperconvexity and the Bergman distance

Bo-Yong Chen, Yuanpu Xiong

Let $Ω \subset C^{n}$ be a bounded hyperconvex domain admitting a negative plurisubharmonic exhaustion function $u$ such that $- u (z) \leq C exp [- η (lo g (1/ δ_{Ω} (z)))]$ near the bou…

math.DG2026

Removable singularities of Yang-Mills-Higgs fields in higher dimensions

Bo Chen

This paper establishes decay estimates near isolated singularities for $n$ -dimensional Yang-Mills-Higgs fields defined on a fiber bundle ( $n \geq 4$ ). These estimates yield a remov…

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.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.CV2024

Density in weighted Bergman spaces and Bergman completeness of Hartogs domains

Bo-Yong Chen, John Erik Fornæss, Jujie Wu

We study the density of functions which are holomorphic in a neighbourhood of the closure $Ω$ of a bounded non-smooth pseudoconvex domain $Ω$ , in the Bergman space $ H^2(Ω…

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

The theorems of M. Riesz and Zygmund in several complex variables

Bo-Yong Chen

In this note, we extend the well-known theorems of M. Riesz and Zygmund on conjugate functions as follows. Let $Ω$ be a domain in $C^{n}$ . Suppose that $f=u+iv\in \mathcal 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…

Quantitative hyperconvexity and the Bergman distance

Removable singularities of Yang-Mills-Higgs fields in higher dimensions

An estimate of the Bergman distance on Riemann surfaces

Real Variable Things in Bergman Theory

Type problem, the first eigenvalue and Hardy inequalities

Density in weighted Bergman spaces and Bergman completeness of Hartogs domains

Type problem and the first eigenvalue

The theorems of M. Riesz and Zygmund in several complex variables

Regularity of the p−Bergman kernel

Regularity of the $p -$ Bergman kernel