Author

Li Sheng

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Preprint Oct 2026

Interior $C^2$ Estimates and a Liouville Theorem for the Complex Monge--Amp\`ere Equation

We establish an interior $C^2$ estimate for locally bounded plurisubharmonic Bedford-Taylor solutions of the complex Monge--Amp\`ere equation $\det(u_{i\bar j})=f$ under weak quadratic growth bounds on sufficiently large balls, where $f$ is positive and Dini-continuous. We assume a distributional lower bound for the La...

Jing-Chen Hu, Li Sheng · 0 citations

Preprint Sep 2026

Pogorelov interior estimates and a Liouville theorem for the complex Monge--Amp\`ere equation

We prove a Pogorelov interior estimate for strictly plurisubharmonic solutions of the complex Monge-Amp\`ere equation $\det(u_{i\bar{j}})=1$ with homogeneous Dirichlet data under the condition that, for some constant $\kappa\geq 1$, $(\kappa u_{i\bar{j}}-u_{is}u^{s\bar{t}}u_{\overline{tj}})$ is non-negative definite. F...

Hong-Yu Chen, Jing-Chen Hu, Li Sheng · 0 citations