We prove uniform gradient and diameter estimates for a family of geometric complex Monge-Ampère equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge-Ampère equations. We also prove a uniform diameter estimate for collapsing families of twisted Kähler-Einstein metrics on Kähler manifolds of nonnegative Kodaira dimensions.
All Science Journal Classification (ASJC) codes
- Applied Mathematics