2024/10/06 by Liu, Junbang · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2410.04395
We prove an Alexandrov-Bakelman-Pucci type estimate, which involves the integral of the determinant of the complex Hessian over a certain subset. It improves the classical ABP estimate adapted (by inequality 22n|det(u_ij)|2≥ |det(∇2u)|) to complex setting. We give an application of it to derive sharp gradient estimates for complex Monge-Ampère equations. The approach is based on the De Giorgi iteration method developed by Guo-Phong-Tong for equations of complex Monge-Ampère type.