Year: 2026
Type: preprint
Abstract: We prove a uniform $L^\infty$-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.
Source: arXiv (Cornell University)
Author: Han, Jiyuan
Institution: Westlake University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7219155345