A uniform L∞ estimate for complex Monge-Ampère equations

Sławomir Kołodziej; Gang Tian

doi:10.1007/s00208-008-0256-x

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

Sławomir Kołodziej
, Gang Tian

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We show a priori L ^∞ estimates for the solutions of the complex Monge-Ampère equation with respect to a sequence of Kähler forms degenerating in the limit. This is applied to prove the existence of generalized Kähler-Einstein metrics for some holomorphic fibrations by Calabi-Yau manifolds.

Original language	English (US)
Pages (from-to)	773-787
Number of pages	15
Journal	Mathematische Annalen
Volume	342
Issue number	4
DOIs	https://doi.org/10.1007/s00208-008-0256-x
State	Published - Dec 2008

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00208-008-0256-x

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title = "A uniform L∞ estimate for complex Monge-Amp{\`e}re equations",

abstract = "We show a priori L ∞ estimates for the solutions of the complex Monge-Amp{\`e}re equation with respect to a sequence of K{\"a}hler forms degenerating in the limit. This is applied to prove the existence of generalized K{\"a}hler-Einstein metrics for some holomorphic fibrations by Calabi-Yau manifolds.",

author = "S{\l}awomir Ko{\l}odziej and Gang Tian",

note = "Funding Information: S. Ko{\l}odziej partially supported by EU grant MTKD-CT-2006-042360 and Polish grants 189/6 PR UE/2007/7, 3679/B/H03/2007/33.",

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N2 - We show a priori L ∞ estimates for the solutions of the complex Monge-Ampère equation with respect to a sequence of Kähler forms degenerating in the limit. This is applied to prove the existence of generalized Kähler-Einstein metrics for some holomorphic fibrations by Calabi-Yau manifolds.

AB - We show a priori L ∞ estimates for the solutions of the complex Monge-Ampère equation with respect to a sequence of Kähler forms degenerating in the limit. This is applied to prove the existence of generalized Kähler-Einstein metrics for some holomorphic fibrations by Calabi-Yau manifolds.

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

Abstract

All Science Journal Classification (ASJC) codes

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