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Parabolic Monge-Ampère equations on a family of Calabi-Yau manifolds
Abstract
We prove a uniform L∞-estimate for the parabolic Monge--Ampère equation under uniform Hörmander-Tian type estimates with respect to the initial and prescribed measures. We apply this estimate to rescaled Kähler--Ricci flows on a family of polarized Calabi--Yau manifolds over the punctured disk. An interpolation argument gives uniform Hörmander-Tian type 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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BibTeX
@misc{han2026parabolic,
title = {{Parabolic Monge-Ampère equations on a family of Calabi-Yau manifolds}},
author = {Jiyuan Han},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01202},
eprint = {2610.01202},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01202},
}
RIS
TY - UNPB
TI - Parabolic Monge-Ampère equations on a family of Calabi-Yau manifolds
AU - Jiyuan Han
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.01202
UR - https://arxiv.org/abs/2610.01202
AB - We prove a uniform L^∞-estimate for the parabolic Monge--Ampère equation under uniform Hörmander-Tian type estimates with respect to the initial and prescribed measures. We apply this estimate to rescaled Kähler--Ricci flows on a family of polarized Calabi--Yau manifolds over the punctured disk. An interpolation argument gives uniform Hörmander-Tian type 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.
ER -