W. Dong

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20242026

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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.AP2026

A Liouville-type theorem for $2$ -Monge-Ampère equation in dimension three

Weisong Dong

We prove that every entire solution with quadratic growth, lying in a suitable cone, to the 2-Monge-Ampère equation on $R^{3}$ is a quadratic polynomial. The proof proceeds…

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

A Liouville-type theorem for 2-Monge-Ampère equation in dimension three

A Liouville-type theorem for $2$ -Monge-Ampère equation in dimension three