FIK blow-down singularities form from an open family of nearby Ricci flow initial data on any closed four-manifold, and nearby flows carry a local first-order asymptotic coordinate.
Non-collapsed finite time singularities of the Ricci flow on compact K\"ahler surfaces are of Type I
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abstract
We show that any non-collapsed finite time singularity of the Ricci flow on a compact K\"ahler surface is of Type I. Combined with a previous result of the first author, Cifarelli, and Deruelle, it follows that any such singularity is modeled on the shrinking Ricci soliton of Feldman-Ilmanen-Knopf on the total space of the line bundle $\mathcal{O}_{\mathbb{P}^1}(-1)\to\mathbb{P}^{1}$.
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math.DG 1years
2026 1verdicts
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Open full-metric formation and local marked first-order asymptotic moduli of FIK blowdown singularities
FIK blow-down singularities form from an open family of nearby Ricci flow initial data on any closed four-manifold, and nearby flows carry a local first-order asymptotic coordinate.