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arXiv · 2408.15269

L^2-instability of the Taub-Bolt metric under the Ricci flow

John Hughes
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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 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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John Hughes. 2024-08-12. L^2-instability of the Taub-Bolt metric under the Ricci flow. https://arxiv.org/abs/2408.15269

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