A uniform L^{\infty} estimate for complex Monge-Ampere equations
Differential Geometry
2007-10-08 v1 Complex Variables
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).
Cite
@article{arxiv.0710.1144,
title = {A uniform L^{\infty} estimate for complex Monge-Ampere equations},
author = {Slawomir Kolodziej and Gang Tian},
journal= {arXiv preprint arXiv:0710.1144},
year = {2007}
}
Comments
14 pages