Yuanpu Xiong

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20192026

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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.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…