Year: 2026
Type: preprint
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 $\operatorname{Tot}(\mathcal{O}_{\mathbb{P}^{n-1}}(-1))$.
Source: arXiv (Cornell University)
Authors: Xu, Tongxin, Zhang, Zhenlei
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203763573