L²-instability of the Taub-Bolt metric under the Ricci flow

2024/08/12 by Hughes, John
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.15269

Abstract

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 L²-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 Ważewski box argument, Ricci flows on compact manifolds which encounter finite singularities modelled on a given asymptotically conical shrinking soliton.

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