8 papers
Existence and Nonexistence for Hessian Exterior Dirichlet Problems with \(k\)-Admissible Asymptotic Matrices
Jiguang Bao, Qinfeng Jiang
We study exterior Dirichlet problems for \(k\)-Hessian equations with prescribed quadratic asymptotics, allowing the asymptotic matrix to be merely \(k\)-admissible and not necessa…
Optimal Asymptotic Behavior at Infinity for Solutions of the Supercritical Lagrangian Mean Curvature Equation in Exterior Domains
Jiguang Bao, Qinfeng Jiang
We study the asymptotic behavior at infinity of solutions to the supercritical Lagrangian mean curvature equation \[ \sum_{i=1}^n \arctan λ_i(D^2u)=θ+f(x) \] on exterior domains…
The mean curvature type hypersurfaces with prescribed gradient image
Jiguang Bao, Rongli Huang, Qinfeng Jiang
In this paper, we consider the existence of mean curvature type hypersurfaces with prescribed gradient image. Let and be uniformly convex bounded domains in $\mathb…
On the second boundary value problem for Lagrangian mean curvature type equation
Jiguang Bao, Qinfeng Jiang
This article is concerned with the second boundary value problem of the Lagrangian mean curvature type equation arising from special Lagrangian geometry. By the parabolic method, w…
Lagrangian Mean Curvature Equations on exterior domains
Jiguang Bao, Qinfeng Jiang
We introduce an extended exterior --quasiconformal mapping method to study the asymptotic behavior at infinity of solutions to the supercritical phase Lagrangi…
A Liouville theorem for ancient solutions of the parabolic Monge-Ampère equation with periodic data
Kui Yan, Jiguang Bao
This article is concerned with the parabolic Monge-Ampère equation , where and are positive periodic functions. We prove that any cla…