5 papers
Siu's curvature positivity and extension theorems for -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 , this operator reduces to the classi…
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 differ…
-estimates on flat vector bundles and Prékopa's theorem
Gang Huang, Weiwen Jiang, Xiangsen Qin
In this paper, we will construct Hörmander's -estimate of the operator on a flat vector bundle over a -convex Riemannian manifold and discuss some geometric applicatio…
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…
Uniform estimates of Green functions and Sobolev-type inequalities on real and complex manifolds
Fusheng Deng, Gang Huang, Xiangsen Qin
We prove certain Sobolev-type and Poincaré-type inequalities for functions on real and complex manifolds for the gradient operator , the Laplace operator , and t…