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arXiv · 2508.20933

Hölder estimates for degenerate complex Monge-Ampère equations

Bin Guo·Slawomir Kolodziej·Jian Song·Jacob Sturm
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Abstract

Uniform $L^\infty$ and Hölder estimates were proved by the Kolodziej for complex Monge-Ampère equations on compact Kähler manifolds with $L^p$ volume measure with $p>1$. On the other hand, establishing Hölder estimates on singular Kähler varieties has remained open. In this paper, we establish uniform Hölder continuity for a family of complex Monge-Ampère equations on Kähler varieties, by developing a geometric regularization based on the partial $C^0$ estimate, i.e., quantitive Kodaira embeddings. As an application, we prove that local potentials of smoothable Kähler-Einstein varieties are Hölder continuous.

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Bin Guo, Slawomir Kolodziej, Jian Song, Jacob Sturm. 2025-08-28. Hölder estimates for degenerate complex Monge-Ampère equations. https://arxiv.org/abs/2508.20933

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