45 citations · 52 across the 14 of their papers we have counts for
17 papers
Boundary regularity of -Hessian eigenfunctions
Guohuan Qiu, Jin Yan
We prove smoothness up to the boundary for -Hessian eigenfunctions on smooth bounded uniformly convex domains when . This resolves an open problem in the regularity t…
Interior estimates for Hessian quotient equations
Guohuan Qiu, Jin Yan
We prove interior Hessian estimates in arbitrary dimensions for admissible solutions of Hessian quotient equations with constant right-hand side, when the numerator and denominator…
Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions
Guohuan Qiu, Jin Yan
We resolve the long-standing problem of establishing interior \(C^2\) estimates for admissible solutions of the graphical scalar curvature equation in every dimension \(n\ge 3\). M…
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…
A Brunn--Minkowski inequality and Convexity for the 2-Hessian eigenvalue in convex domains
Jiahuan Li, Xi-Nan Ma, Guohuan Qiu +1
We prove the strict log-concavity of the positive first eigenfunction \(-u\) of the \(2\)-Hessian equation and the strict -convexity of the solution for the corresponding tors…
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…
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…
Very weak solutions of the Dirichlet problem for 2-Hessian equation
Tongtong Li, Guohuan Qiu
For any small, we construct infinitely many very weak solutions to the 2-Hessian equation with prescribed boundary value. The proof relies on the convex integration m…
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…
Interior curvature estimates for hypersurfaces of prescribing scalar curvature in dimension three
Guohuan Qiu
We prove a priori interior curvature estimates for hypersurfaces of prescribing scalar curvature equations in dimension three. The method is motivated by the integral method of War…
Interior Hessian estimates for Sigma-2 equations in dimension three
Guohuan Qiu
We prove a priori interior C2 estimate for σ_2 = f in R3, which generalizes Warren-Yuan's result.
Interior C2 regularity of convex solutions to prescribing scalar curvature equations
Pengfei Guan, Guohuan Qiu
We establish interior estimates for convex solutions of scalar curvature equation and -Hessian equation. We also prove interior curvature estimate for isometrically imme…
Classical Neumann Problems for Hessian equations and Alexandrov-Fenchel's inequalities
Guohuan Qiu, Chao Xia
Recently, the first named author together with Xinan Ma \cite{ma2015neumann}, have proved the existence of the Neumann problems for Hessian equations. In this paper, we proceed fur…
The Neumann Problem for Hessian Equations
Xi-Nan Ma, Guohuan Qiu
In this paper, we prove the existence of a classical solution to a Neumann boundary problem for Hessian equations in uniformly convex domain. The methods depend upon the establishe…
A generalization of Reilly's formula and its applications to a new Heintze-Karcher type inequality
Guohuan Qiu, Chao Xia
In this paper, we prove a generalization of Reilly's formula in \cite{Reilly}. We apply such general Reilly's formula to give alternative proofs of the Alexandrov's Theorem and the…