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Mathematics > Differential Geometry

arXiv:0710.1144 (math)
[Submitted on 5 Oct 2007]

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

Authors:Slawomir Kolodziej, Gang Tian
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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).
Comments: 14 pages
Subjects: Differential Geometry (math.DG); Complex Variables (math.CV)
MSC classes: 53C25; 32U
Cite as: arXiv:0710.1144 [math.DG]
  (or arXiv:0710.1144v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.1144

Submission history

From: Sł awomir Koł odziej [view email]
[v1] Fri, 5 Oct 2007 08:16:09 UTC (10 KB)
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