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Giovanni, Francesco Di

doi:10.1016/j.aim.2021.107621

Cited by 2 publications

(1 citation statement)

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“…Motivated by his theory, the results developed by Angenent and Knopf in [2], as well as several recent examples of Type II singularities, e.g. [3,4,18,40,46], we introduce a local analysis of singularities and curvature blow-up rates.…”

Section: A Refined Local Singularity Analysismentioning

confidence: 99%

A local singularity analysis for the Ricci flow and its applications to Ricci flows with bounded scalar curvature

Buzano

Matteo

2022

Calc. Var.

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We develop a refined singularity analysis for the Ricci flow by investigating curvature blow-up rates locally. We first introduce general definitions of Type I and Type II singular points and show that these are indeed the only possible types of singular points. In particular, near any singular point the Riemannian curvature tensor has to blow up at least at a Type I rate, generalising a result of Enders, Topping and the first author that relied on a global Type I assumption. We also prove analogous results for the Ricci tensor, as well as a localised version of Sesum’s result, namely that the Ricci curvature must blow up near every singular point of a Ricci flow, again at least at a Type I rate. Finally, we show some applications of the theory to Ricci flows with bounded scalar curvature.

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Section: A Refined Local Singularity Analysismentioning

confidence: 99%

A local singularity analysis for the Ricci flow and its applications to Ricci flows with bounded scalar curvature

Buzano

Matteo

2022

Calc. Var.

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Convergence of Ricci flow solutions to Taub-NUT

Giovanni

2021

Communications in Partial Differential Equations

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We study the Ricci flow starting at an SU(2) cohomogeneity-1 metric g 0 on R 4 with monotone warping coefficients and whose restriction to any hypersphere is a Berger metric. If g 0 has bounded Hopf-fiber, curvature controlled by the size of the orbits and opens faster than a paraboloid in the directions orthogonal to the Hopf-fiber, then the flow converges to the Taub-NUT metric g TNUT in the Cheeger-Gromov sense in infinite time. We also classify the long-time behaviour when g 0 is asymptotically flat. In order to identify infinite-time singularity models we obtain a uniqueness result for g TNUT : ARTICLE HISTORY

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Rotationally symmetric Ricci flow on Rn+1

Cited by 2 publications

References 24 publications

A local singularity analysis for the Ricci flow and its applications to Ricci flows with bounded scalar curvature

A local singularity analysis for the Ricci flow and its applications to Ricci flows with bounded scalar curvature

Convergence of Ricci flow solutions to Taub-NUT

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