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

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

2007-10-05

arxiv.org/abs/0710.1144v1

Mathematics

Differential Geometry

14 pages

Scientific paper

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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