English

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).

Keywords

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

R2 v1 2026-06-21T09:27:09.015Z