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arXiv · 2509.14820

Laplace comparison on K\"ahler Ricci flow and convergence

Gang Tian·Qi S. Zhang·Zhenlei Zhang·Meng Zhu·Xiaohua Zhu
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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.

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Gang Tian, Qi S. Zhang, Zhenlei Zhang, Meng Zhu, Xiaohua Zhu. 2025-09-18. Laplace comparison on K\"ahler Ricci flow and convergence. https://arxiv.org/abs/2509.14820

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