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…

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

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