Yuanpu Xiong

activity

20242026

collaborators

5 papers

math.CV2026

Convexity of the Bergman Kernels on Convex Domains

Yuanpu Xiong

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

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 $I^»_{1} (M) > 0$ . Let $I ¨ $ denote the distance from a fixed point $x_{0} \in M$ and $r_{x}$ the injectivity radius at $x$ .…

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…