Siyuan Lu

activity

20242026

collaborators

3 papers

math.AP2026

On Liouville's theorem for the Hessian quotient equation $I ¨ _{2} / I ¨ _{1}$

Siyuan Lu, Marcin Sroka

We prove Liouville's theorem for semi-convex entire solutions to Hessian quotient equation $I ¨ _{2} / I ¨ _{1} = 1$ in $R^{n}$ . The proof is based on the observation that after rewriti…

math.AP2025

Pogorelov type interior $C^{2}$ estimate for Hessian quotient equation and its application

Siyuan Lu, Yi-Lin Tsai

In this paper, we derive a Pogorelov type interior $C^{2}$ estimate for the Hessian quotient equation $\frac{I ¨ _{n}}{I ¨ _{k}} (D^{2} u) = f$ . As an application, we show that convex…

math.AP2024

A simple proof of curvature estimates for the n-1 Hessian equation

Siyuan Lu, Yi-Lin Tsai

In [Amer. J. Math. 141 (2019), no. 5, 1281-1315], Ren and Wang proved the curvature estimates for the $n - 1$ curvature equation. The purpose of this note is to give a simple proof o…

On Liouville's theorem for the Hessian quotient equation I¨2​/I¨1​

Pogorelov type interior C2 estimate for Hessian quotient equation and its application

A simple proof of curvature estimates for the n-1 Hessian equation

On Liouville's theorem for the Hessian quotient equation $I ¨ _{2} / I ¨ _{1}$

Pogorelov type interior $C^{2}$ estimate for Hessian quotient equation and its application