Cheuk-Yan Fung

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20212026

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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…

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