Laplace comparison on K\"ahler Ricci flow and convergence
Differential Geometry
2025-10-30 v2
Abstract
We first prove a uniform integral Laplace comparison result for the K\"ahler Ricci flow on Fano manifolds which depends only on the initial metric. As an application, using Cheeger-Colding theory and previous results by some of the authors, we give a direct and independent proof of the Hamilton-Tian conjecture on convergence of K\"ahler-Ricci flows, modulo a codimension 4 singular set. We also expounded on some existing literature on this conjecture.
Cite
@article{arxiv.2509.14820,
title = {Laplace comparison on K\"ahler Ricci flow and convergence},
author = {Gang Tian and Qi S. Zhang and Zhenlei Zhang and Meng Zhu and Xiaohua Zhu},
journal= {arXiv preprint arXiv:2509.14820},
year = {2025}
}
Comments
43 pages. replaces the appendix by a remark and link