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arXiv · 2610.01202

Parabolic Monge-Ampère equations on a family of Calabi-Yau manifolds

Jiyuan Han
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Abstract

We prove a uniform $L^\infty$-estimate for the parabolic Monge--Ampère equation under uniform Skoda estimates with respect to the initial and prescribed measures. We apply this estimate to Kähler--Ricci flows on a family of polarized Calabi--Yau manifolds over the punctured disk. An interpolation argument gives uniform Skoda estimates along the flows. We also establish uniform diameter bounds and Gromov--Hausdorff precompactness for this family of flows. In particular, we obtain an alternative proof of the diameter estimate by Li-Tosatti.

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Jiyuan Han. 2026-10-01. Parabolic Monge-Ampère equations on a family of Calabi-Yau manifolds. https://arxiv.org/abs/2610.01202

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