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Geometric estimates for complex Monge-Ampere equations

Xin Fu Rutgers University Bin Guo Columbia University Jian Song Rutgers University

Analysis of PDEs mathscidoc:2005.03002

Silver Award Paper in 2020

Journal für die reine und angewandte Mathematik
We prove uniform gradient and diameter estimates for a family of geometric complex Monge–Ampere equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge–Ampere equations. We also prove a uniform diameter estimate for collapsing families of twisted Kahler–Einstein metrics on Kahler manifolds of nonnegative Kodaira dimensions.
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  • To appear in Journal für die reine und angewandte Mathematik
@inproceedings{xingeometric,
  title={Geometric estimates for complex Monge-Ampere equations},
  author={Xin Fu, Bin Guo, and Jian Song},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200513002636723666672},
  booktitle={Journal für die reine und angewandte Mathematik},
}
Xin Fu, Bin Guo, and Jian Song. Geometric estimates for complex Monge-Ampere equations. In Journal für die reine und angewandte Mathematik. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200513002636723666672.
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