Geometric estimates for complex Monge–Ampère equations

By Xin Fu, Bin Guo, Jian Song. Journal für die Reine und Angewandte Mathematik, 2017

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Abstract 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0ccbe7158de8cfa53f5df01940c793192c73aef5