Log continuity of solutions of complex Monge-Ampère equations

Let X be a compact Kaehler manifold with semipositive anticanonical line bundle. Let L be a big and semi-ample line bundle on X and \(\alpha\) be the Chern class of L. We prove that the solution of the complex Monge-Ampère equations in \(\alpha\) with Lp righthand side (p > 1) is \(\log^M\)-conti...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Hoang-Son Do, Duc-Viet Vu
Format: Article
Language:English
Subjects:
Manifolds
Mathematical analysis
Online Access:Get full text
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Summary:Let X be a compact Kaehler manifold with semipositive anticanonical line bundle. Let L be a big and semi-ample line bundle on X and \(\alpha\) be the Chern class of L. We prove that the solution of the complex Monge-Ampère equations in \(\alpha\) with Lp righthand side (p > 1) is \(\log^M\)-continuous for every constant M > 0. As an application, we show that every singular Ricci-flat metric in a semi-ample class in a projective Calabi-Yau manifold X is globally \(\log^M\)-continuous with respect to a smooth metric on X.
ISSN:2331-8422