Cheuk-Yan Fung

activity

20212026

collaborators

4 papers

math.AP2026

Doubling Argument of the Hessian Estimate for the Hessian Quotient Equations

Cheuk Yan Fung

In this paper, we establish a doubling argument to obtain Hessian estimates for convex solutions to the Hessian quotient equation $\frac{σ _{n}}{σ _{k}} (D^{2} u) = f (x, u, D u)$ for $k = n - 1$ an…

math.AP2026

On Counterexamples to Interior $C^{2}$ Estimates for Monge-Ampère Type Equations

Cheuk Yan Fung

We modify Pogorelov's classic construction to demonstrate the absence of a priori $C^{2}$ estimates for the equations $det (D^{2} u \pm D u \otimes D u) = f (x)$ in dimension $n \geq 3$ . W…

math.AP2025

Doubling Argument of the Hessian Estimate for the Special Lagrangian Equation on General Phases with Constraints

Cheuk Yan Fung

In this paper, we establish a doubling argument to obtain Hessian estimates for the special Lagrangian equation under general phase constraints. In particular, our approach does no…

math.DG2021

On the Ricci curvature of Kahler-Ricci Flow

Cheuk Yan Fung

In this paper, we consider $n$ -dimensional compact K $a ¨$ hler manifold with semi-ample canonical line bundle under the long time solution of K $a ¨$ hler Ricci Flow. In par…

Doubling Argument of the Hessian Estimate for the Hessian Quotient Equations

On Counterexamples to Interior C2 Estimates for Monge-Ampère Type Equations

Doubling Argument of the Hessian Estimate for the Special Lagrangian Equation on General Phases with Constraints

On the Ricci curvature of Kahler-Ricci Flow

On Counterexamples to Interior $C^{2}$ Estimates for Monge-Ampère Type Equations