Fusheng Deng

activity

20242026

collaborators

8 papers

math.CV2026

An Exact Spherical-Solid Mean Formula and Vanishing Criteria for Lelong Numbers

Fusheng Deng, Yizhe Yang, Zhanpeng You

We establish an exact additive formula expressing the Lelong number of a plurisubharmonic function in terms of the limiting difference between its spherical and solid means. Buildi…

math.CV2026

Holomorphic Approximation for Real Diffeomorphism Groups

Fusheng Deng, Gaofeng Huang, Frank Kutzschebauch +1

We show that every diffeomorphism of $R^{n}$ for $n \geq 2$ can be approximated by an automorphism of $C^{n}$ in the Whitney $C^{k}$ -topology for any positive integer $k…

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.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…

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.NA2024

Numerical calculation method for function integration on submanifolds of $R^{n}$ or compact Riemannian manifolds

Fusheng Deng, Gang Huang, Yingyi Wu

In this paper, we present a method for digitally representing the "volume element" and calculating the integral of a function on compact hypersurfaces with or without boundary, and…

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

$\partial ˉ$ 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…

An Exact Spherical-Solid Mean Formula and Vanishing Criteria for Lelong Numbers

Holomorphic Approximation for Real Diffeomorphism Groups

Estimates of heat kernels and Sobolev-type inequalities for twisted differential forms on compact Kähler manifolds

Dirichlet Green kernel estimates and Sobolev-type inequalities for twisted differential forms

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

Numerical calculation method for function integration on submanifolds of Rn or compact Riemannian manifolds

A bridge connecting convex analysis and complex analysis and L2-estimate of d and ∂ˉ

∂ˉ Sobolev-type inequality and an improved L2-estimate of ∂ˉ on bounded strictly pseudoconvex domains

Numerical calculation method for function integration on submanifolds of $R^{n}$ or compact Riemannian manifolds

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