A uniform L^∞ estimate for complex Monge-Ampere equations

2007/10/05 by Kolodziej, Slawomir, Tian, Gang
#32U #53C25 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0710.1144

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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