Xingchen Zhou

activity

20202026

most citedHessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase

1 citations · 1 across the 11 of their papers we have counts for

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math.AP2026

Rigidity for Convex Entire Solutions to the $k$ -Hessian Equation

Xingchen Zhou, Ruixuan Zhu

We prove that for each $3 \leq k \leq n - 1$ a convex $C^{2}$ entire solution of $σ_{k}$ equation in $R^{n}$ with positive constant right hand side is a quadratic polynomial, without…

math.AP2026

Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase

Ruosi Chen, Xingchen Zhou, Ruixuan Zhu

Let $n \geq 3$ . We prove a priori interior gradient estimate for the Lagrangian mean curvature equation \[ \sum_{i=1}^n\arctanλ_i(D^2u)=θ(x) \] under the critical and supercritical ph…

math.AP2026

Interior $C^{2, α}$ Regularity for the Quadratic Hessian Equation

Ruosi Chen, Xingchen Zhou, Ruixuan Zhu

We establish interior $C^{2, α}$ regularity for admissible solutions of the quadratic Hessian equation with positive $C^{α}$ right-hand side on the full positive branch. The main ingr…

math.AP2026

Regularity for convex viscosity solutions of $σ_{3}$ equation

Ruosi Chen, Yannan Liu, Xingchen Zhou

We prove interior $C^{2}$ regularity for convex viscosity solutions of the $3$ -Hessian equation $σ_{3} (D^{2} u) = f (x)$ with $f \in C^{0, 1}, in f f > 0$ , under a strict $3$ -convexity condition…

math.AP2026

Interior $C^{2, α}$ Regularity for Convex Solutions of the 2-Hessian Equation

Xingchen Zhou, Ruixuan Zhu

We consider convex admissible viscosity solutions of $σ_{2} (D^{2} u) = f > 0$ in an open subset of $R^{n}$ , where $n \geq 2$ , $0 < α < 1$ , and $f \in C_{loc}^{0, α}$ . We prove that ev…

math.AP2026

Regularity for convex viscosity solutions of $σ_{2}$ Equation

Ruosi Chen, Huaiyu Jian, Xushan Tu +1

We prove interior $C^{2}$ regularity result for convex viscosity solutions of the quadratic Hessian equation $σ_{2} (D^{2} u) = f (x)$ , under the assumption that $f \in C^{0, 1}$ with $\inf…

math.AP2024

New Approach for Interior Regularity of Monge-Ampère Equations

Ruosi Chen, Xingchen Zhou

By developing an integral approach, we present a new method for the interior regularity of strictly convex solution of the Monge-Ampère equation $det D^{2} u = 1$ .

math.AP2024

An Integral Approach to Prescribing Scalar Curvature Equations

Ruosi Chen, Huaiyu Jian, Xingchen Zhou

We develop an integral approach to obtain interior a priori $C^{1, 1}$ estimates for convex solutions of prescribing scalar curvature equations $σ_{2} (κ) = f (x)$ as well as the Hessia…

math.AP2024

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…

math.AP2023

Notes on generalized special Lagrangian equation

Xingchen Zhou

We obtain a prior $C^{1, 1}$ estimates for some Hessian (quotient) equations with positive Lipschitz right hand sides, through studying a twisted special Lagrangian equation. The re…

math.AP2023★ 1 cited

Hessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase

Xingchen Zhou

We establish a prior interior $C^{1, 1}$ estimates for convex solutions and supercritical phase solutions to the Lagrangian mean curvature equation with sharp Lipschitz phase. Count…

Rigidity for Convex Entire Solutions to the k-Hessian Equation

Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase

Interior C2,α Regularity for the Quadratic Hessian Equation

Regularity for convex viscosity solutions of σ3​ equation

Interior C2,α Regularity for Convex Solutions of the 2-Hessian Equation

Regularity for convex viscosity solutions of σ2​ Equation

New Approach for Interior Regularity of Monge-Ampère Equations

An Integral Approach to Prescribing Scalar Curvature Equations

A priori interior estimates for special Lagrangian curvature equations

Notes on generalized special Lagrangian equation

Hessian estimates for Lagrangian mean curvature equation with sharp Lipschitz phase

Rigidity for Convex Entire Solutions to the $k$ -Hessian Equation

Interior $C^{2, α}$ Regularity for the Quadratic Hessian Equation

Regularity for convex viscosity solutions of $σ_{3}$ equation

Interior $C^{2, α}$ Regularity for Convex Solutions of the 2-Hessian Equation

Regularity for convex viscosity solutions of $σ_{2}$ Equation