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arXiv · 2608.17458

Finite Time Type I Singularities of the Kähler Ricci Flow

Tongxin Xu·Zhenlei Zhang
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Abstract

We prove the Feldman--Ilmanen--Knopf conjecture for finite time Type I singularities of the Kähler--Ricci flow. More precisely, for any compact Kähler manifold $Y$ and its blow-up $π:\operatorname{Bl}_pY\longrightarrow Y$, if $[ω_0]-Tc_1(M)=π^*[ω_Y]$, then any Type I parabolic blow-up limit of the Kähler Ricci flow along the exceptional divisor is the FIK shrinker $\operatorname{Tot}(\mathcal{O}_{\mathbb{P}^{n-1}}(-1))$.

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Tongxin Xu, Zhenlei Zhang. 2026-09-04. Finite Time Type I Singularities of the Kähler Ricci Flow. https://arxiv.org/abs/2608.17458

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