%0 Journal Article
%T A uniform L^{\infty} estimate for complex Monge-Ampere equations
%A Slawomir Kolodziej
%A Gang Tian
%J Mathematics
%D 2007
%I arXiv
%X 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).
%U http://arxiv.org/abs/0710.1144v1