Xiangsen Qin

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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.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…

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

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

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