Gang Huang

activity

20242026

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math.CV2026

Siu's curvature positivity and $L^{2}$ extension theorems for $(p, q)$ -forms

Gang Huang

In this paper, we introduce Siu's curvature operator $A^E_{p,q}$ for vector-bundle-valued differential forms on Kähler manifolds. When $p = n$ , this operator reduces to the classic…

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…

Siu's curvature positivity and L2 extension theorems for (p,q)-forms

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

Siu's curvature positivity and $L^{2}$ extension theorems for $(p, q)$ -forms