7 papers
Robin and Neumann problems for the graph scalar curvature equation
Guohuan Qiu
We study Robin and Neumann problems for the scalar curvature equation of admissible graphs over bounded uniformly convex domains in three dimensions. Under a small-volume assumptio…
Nonconvex Sublevel Sets for the Three-Dimensional Special Lagrangian Equation
Guohuan Qiu
For each phase , we construct a smooth, bounded, uniformly convex domain in for which the zero-Dirichlet solution of the special Lagrangian equation has…
Nonconvex Sublevel Sets For The Planar Translating Mean Curvature Equation
Jiahuan Li, Yilu Liu, Xi-Nan Ma +1
Translating solitons arise as models for type~II singularities of mean-convex mean curvature flow. We construct a smooth bounded uniformly convex domain \(\Om\Subset\R^2\) such tha…
Some counterexamples for the special lagrangian curvature equation
Guohuan Qiu, Guanyu Tao
We construct three counterexamples for the special Lagrangian curvature equation (SLCE). First, in dimension two, we use a post-focal branch of a parallel surface with constant pos…
The Neumann problem of special Lagrangian type equations
Guohuan Qiu, Dekai Zhang
We study the Neumann problem for special Lagrangian type equations with critical and supercritical phases. These equations naturally generalize the special Lagrangian equation and…
A priori interior estimates for special Lagrangian curvature equations
Guohuan Qiu, Xingchen Zhou
We establish a priori interior curvature estimates for the special Lagrangian curvature equations in both the critical phase and convex case. Additionally, we prove a priori interi…