Geometric Estimates for Complex Monge-Ampere Equations

Abstract: We prove uniform gradient and diameter estimates for a family of geometric complex Monge-Amp`ere equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge-Amp`ere equations. We also prove a uniform diameter estimate for collapsing families of twisted K¨ahler-Einstein metrics on K¨ahler manifolds of nonnegative Kodaira dimensions. This is a joint work with Bin Guo and Jian Song.

Mathematics

Audience: researchers in the topic

ICCM 2020