Xiangsen Qin

activity

20242026

collaborators

11 papers

math.AG2026

Dolbeault Cohomology Growth under Curvature Rank Bounds

Xiangsen Qin

Let $L$ be a smooth Hermitian holomorphic line bundle on a compact complex manifold $X$ of dimension $n$ , and let $r$ be its maximal curvature rank. For every fixed holomorphic vec…

math.AG2026

Failure of local extension of semipositive metrics in a smooth projective family

Xiangsen Qin

We construct a smooth projective family of rational surfaces and an effective line bundle on its total space that give a negative answer to Păun's metric-extension question. The re…

math.DG2026

Chern Holomorphic Sectional Curvature: Canonical Ampleness, Rigidity, and Flatness Counterexamples

Xiangsen Qin, Yuanhong Tian

Let $X$ be a compact Brody-hyperbolic complex manifold admitting a strictly positive real $(1, 1)$ -current $T$ with smooth $d T$ and $d d^{c} T \leq 0$ . We prove that the canonical bundle $…

math.CV2025

Quantitative Carleman-type estimates for holomorphic sections over bounded domains

Xiangsen Qin

This paper establishes quantitative Carleman-type inequalities for holomorphic sections of Hermitian vector bundles over bounded domains in $C^{n}$ with $n \geq 2$ . We first…

math.CV2025

Estimates of heat kernels and Sobolev-type inequalities for twisted differential forms on compact Kähler manifolds

Fusheng Deng, Gang Huang, Xiangsen Qin

The main goal of this paper is to generalize the Sobolev-type inequalities given by Guo-Phong-Song-Sturm and Guedj-Tô from the case of functions to the framework of twisted differe…

math.DG2025

$L^{2}$ -estimates on flat vector bundles and Prékopa's theorem

Gang Huang, Weiwen Jiang, Xiangsen Qin

In this paper, we will construct Hörmander's $L^{2}$ -estimate of the operator $d$ on a flat vector bundle over a $p$ -convex Riemannian manifold and discuss some geometric application…

math.AP2025

Dirichlet Green kernel estimates and Sobolev-type inequalities for twisted differential forms

Fusheng Deng, Gang Huang, Xiangsen Qin

We study the full-trace Dirichlet realization of the Dolbeault Laplacian on differential forms with values in a Hermitian holomorphic vector bundle over a relatively compact smooth…

math.CV2024

Uniform estimates of Green functions and Sobolev-type inequalities on real and complex manifolds

Fusheng Deng, Gang Huang, Xiangsen Qin

We prove certain $L^{p}$ Sobolev-type and Poincaré-type inequalities for functions on real and complex manifolds for the gradient operator $\nabla$ , the Laplace operator $Δ$ , and the…

math.CV2024

A bridge connecting convex analysis and complex analysis and $L^{2}$ -estimate of $d$ and $\partial ˉ$

Fusheng Deng, Jinjin Hu, Weiwen Jiang +1

We propose a way to connect complex analysis and convex analysis. As applications, we derive some results about $L^{2}$ -estimate for $d$ -equation and prove some curvature positivity…

math.CV2024

Curvature formulas and curvature strict positivity of direct image bundles

Xiangsen Qin

In this paper, we consider the curvature strict positivity of direct image bundles (vector bundles) associated to a strictly pseudoconvex family of bounded domains.The main result…

math.CV2024

$\partial ˉ$ Sobolev-type inequality and an improved $L^{2}$ -estimate of $\partial ˉ$ on bounded strictly pseudoconvex domains

Fusheng Deng, Weiwen Jiang, Xiangsen Qin

We prove several Sobolev-type inequalities related to the $\partial ˉ$ -operator on bounded domains in $C^{n}$ , which can be viewed as a $\partial ˉ$ -version of the class…

Dolbeault Cohomology Growth under Curvature Rank Bounds

Failure of local extension of semipositive metrics in a smooth projective family

Chern Holomorphic Sectional Curvature: Canonical Ampleness, Rigidity, and Flatness Counterexamples

Quantitative Carleman-type estimates for holomorphic sections over bounded domains

Estimates of heat kernels and Sobolev-type inequalities for twisted differential forms on compact Kähler manifolds

L2-estimates on flat vector bundles and Prékopa's theorem

Dirichlet Green kernel estimates and Sobolev-type inequalities for twisted differential forms

Uniform estimates of Green functions and Sobolev-type inequalities on real and complex manifolds

A bridge connecting convex analysis and complex analysis and L2-estimate of d and ∂ˉ

Curvature formulas and curvature strict positivity of direct image bundles

∂ˉ Sobolev-type inequality and an improved L2-estimate of ∂ˉ on bounded strictly pseudoconvex domains

$L^{2}$ -estimates on flat vector bundles and Prékopa's theorem

A bridge connecting convex analysis and complex analysis and $L^{2}$ -estimate of $d$ and $\partial ˉ$

$\partial ˉ$ Sobolev-type inequality and an improved $L^{2}$ -estimate of $\partial ˉ$ on bounded strictly pseudoconvex domains