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.
L^2-instability of the Taub-Bolt metric under the Ricci flow
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In this paper we prove that there exists a compact perturbation of the Ricci flat Taub-Bolt metric that evolves under the Ricci flow into a finite time singularity modelled on the shrinking solition FIK [5]. Moreover, this perturbation can be made arbitrarily L^2-small with respect to the Taub-Bolt metric. The method of proof closely follows the strategy adopted in [14], where the author constructs, via a Wa\.zewski box argument, Ricci flows on compact manifolds which encounter finite singularities modelled on a given asymptotically conical shrinking soliton.
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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.