Geometric estimates for complex Monge-Ampère equations

Xin Fu, Bin Guo, Jian Song

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
JournalJournal fur die Reine und Angewandte Mathematik
StateAccepted/In press - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Mathematics(all)

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