Xiangsen Qin

collaborators

4 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 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.CV2024

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