Xiangsen Qin

collaborators

7 papers

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 KÃ¤hler 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-TÃ´ from the case of functions to the framework of twisted differ…

math.CV2025

$\partial ˉ$ 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…

math.CV2025

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.DG2025

Gang Huang, Weiwen Jiang, Xiangsen Qin

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

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…

Quantitative Carleman-type estimates for holomorphic sections over bounded domains

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

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

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

L2-estimates on flat vector bundles and PrÃ©kopa's theorem

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

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

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

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