Mathematische Annalen

, 342:773 | Cite as

A uniform L estimate for complex Monge–Ampère equations

  • Sławomir KołodziejEmail author
  • Gang Tian


We show a priori L estimates for the solutions of the complex Monge–Ampère equation with respect to a sequence of Kähler forms degenerating in the limit. This is applied to prove the existence of generalized Kähler–Einstein metrics for some holomorphic fibrations by Calabi-Yau manifolds.


Manifold Isoperimetric Inequality Schwarz Inequality Einstein Metrics Ideal Sheaf 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institute of MathematicsJagiellonian UniversityKrakowPoland
  2. 2.Department of MathematicsPrinceton University, Fine HallPrincetonUSA

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