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A uniform L ∞ estimate for complex Monge–Ampère equations

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059, Krakow, Poland

    Sławomir Kołodziej

  2. Department of Mathematics, Princeton University, Fine Hall, Princeton, NJ, 08544, USA

    Gang Tian

Authors
  1. Sławomir Kołodziej
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  2. Gang Tian
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Corresponding author

Correspondence to Sławomir Kołodziej.

Additional information

S. Kołodziej 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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Kołodziej, S., Tian, G. A uniform L ∞ estimate for complex Monge–Ampère equations. Math. Ann. 342, 773–787 (2008). https://doi.org/10.1007/s00208-008-0256-x

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  • DOI: https://doi.org/10.1007/s00208-008-0256-x

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