Xiangsen Qin

activity

20242026

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4 papers · 1 filter

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…

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

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