23 citations · 34 across the 12 of their papers we have counts for
14 papers
Shrinking Kähler-Ricci solitons on toric fano fibrations
Tristan C. Collins, Genggeng Huang, Freid Tong +1
We prove that a smooth toric Fano fibration admits a complete gradient shrinking Kähler-Ricci soliton.
Classification of solutions for some mixed order elliptic system
Genggeng Huang, Yating Niu
In this paper, we classify the solution of the following mixed-order conformally invariant system with coupled nonlinearity in : \begin{equation}\left\{ \begin{align…
Regularity of free boundary for the Monge-Ampère obstacle problem
Genggeng Huang, Lan Tang, Xu-Jia Wang
In this paper, we prove the regularity of the free boundary in the Monge-Ampère obstacle problem By duality, the regularity of the free boundary is…
Analyticity of the solutions to degenerate Monge-Ampère equations
Genggeng Huang, Yingshu Lü
This paper is devoted to study the following degenerate Monge-Ampère equation: \begin{eqnarray}\label{ab1} \begin{cases} \det D^2 u=Λ_q (-u)^q \quad \text{in}\quad Ω,\\ u=0 \quad\t…
Coexisting Vortices and Antivortices Generated by Dually Gauged Harmonic Maps
Xiaosen Han, Genggeng Huang, Yisong Yang
In this paper we first formulate a dually gauged harmonic map model, suggested from a product Abelian Higgs field theory arising in impurity-inspired field theories, and obtain a n…
On the Hardy-Littlewood-Sobolev type systems
Ze Cheng, Genggeng Huang, Congming Li
In this paper, we study some qualitative properties of Hardy-Littlewood-Sobolev type systems. The HLS type systems are categorized into three cases: critical, supercritical and sub…
Uniqueness of topological solutions of self-dual Chern-Simons equation with collapsing vortices
Genggeng Huang, Chang-Shou Lin
We consider the following Chern-Simons equation, \begin{equation} \label{0.1} Δu+\frac 1{\varepsilon^2} e^u(1-e^u)=4π\sum_{i=1}^N δ_{p_i^\varepsilon},\quad \text{in}\quad Ω, \end{e…
A Liouville theorem for subcritical Lane-Emden system
Ze Cheng, Genggeng Huang, Congming Li
In this paper, we present a necessary and sufficient condition to the Lane-Emden conjecture. This condition is an energy type of integral estimate on solutions to subcritical Lane-…
A Liouville theorem for high order degenerate elliptic equations
Genggeng Huang, Congming Li
In this paper, we apply the moving plane method to the following high order degenerate elliptic equation,\begin{equation*} (-A)^p u=u^α\text{ in } \mathbb R^{n+1}_+,n\geq 1, \end{e…
Compactness of Alexandrov-Nirenberg Surfaces
Qing Han, Jiaxing Hong, Genggeng Huang
We study a class of compact surfaces in introduced by Alexandrov and generalized by Nirenberg and prove a compactness result under suitable assumptions on induced met…
Existence of non-topological solutions for a skew-symmetric Chern-Simons system
Genggeng Huang, Chang-Shou Lin
We investigate the existence of non-topological solutions satisfying such that and $$(β_1-1…
Existence of the maximizing pair for the discrete Hardy-Littlewood-Sobolev inequality
Genggeng Huang, Congming Li, Ximing Yin
In this paper, we study the best constant of the following discrete Hardy-Littlewood-Sobolev inequality, \begin{equation} \sum_{i,j,i\neq j}\frac{f_{i}g_{j}}{\mid i-j\mid^{n-α}}\le…
A priori bounds for a class of semi-linear degenerate elliptic equations
Genggeng Huang
In this paper, we mainly discuss a priori bounds of the following degenerate elliptic equation, {equation}\label{000} a^{ij}(x)\partial_{ij}u+b^i(x)\partial_i u +f(x,u)=0,\text{in}…
A Liouville theorem of degenerate elliptic equation and its application
Genggeng Huang
In this paper, we apply the moving plane method to some degenerate elliptic equations to get a Liouville type theorem. As an application, we derive the a priori bounds for positive…