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A uniform L^{\infty} estimate for complex Monge-Ampere equations

Authors
  • Kolodziej, Slawomir
  • Tian, Gang
Type
Preprint
Publication Date
Oct 05, 2007
Submission Date
Oct 05, 2007
Source
arXiv
License
Unknown
External links

Abstract

We prove uniform sup-norm estimates for the Monge-Ampere equation with respect to a family of Kahler metrics which degenerate towards a pull-back of a metric from a lower dimensional manifold. This is then used to show the existence of generalized Kahler-Einstein metrics as the limits of the Kahler-Ricci flow for some holomorphic fibrations (in the spirit of Song and Tian "The Kahler-Ricci flow on surfaces of positive Kodaira dimension", arXiv:math/0602150).

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