Ruijia Zhang

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math.AP2026

Interior Hessian estimates for Hessian quotient equations

Weisong Dong, Ruijia Zhang

In this paper, we establish interior $C^{2}$ estimates for admissible semiconvex solutions to the general Hessian quotient equation $\frac{σ _{k}}{σ _{l}} (D^{2} u) = f (x, u),$ for the cases $l=k…

math.AP2026

Second order estimates for equations with sums of Hessian operators on Hermitian manifolds

Weisong Dong, Ruijia Zhang

In this paper, we establish an a priori second-order estimate for admissible solutions satisfying a dynamic plurisubharmonic condition to equations involving sums of Hessian operat…

math.AP2026

Pogorelov interior estimates for sum-of-Hessians equations

Weisong Dong, Sirui Xu, Ruijia Zhang

In this paper, we develop a new approach to sum-of-Hessians equations involving multiple $k$ -Hessian operators of distinct orders. By exploiting the concavity of sums of Hessian op…

math.AP2024

$C^{2}$ estimates for $k$ -Hessian equations and a rigidity theorem

Ruijia Zhang

We derive a concavity inequality for $k$ -Hessian operators under the semi-convexity condition. As an application, we establish interior estimates for semi-convex solutions of the $…

Interior Hessian estimates for Hessian quotient equations

Second order estimates for equations with sums of Hessian operators on Hermitian manifolds

Pogorelov interior estimates for sum-of-Hessians equations

C2 estimates for k-Hessian equations and a rigidity theorem

$C^{2}$ estimates for $k$ -Hessian equations and a rigidity theorem