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R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions

Réalisation : 29 juin 2021 Mise en ligne : 29 juin 2021
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Descriptif

We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a singular set of parabolic codimension at least 4. We furthermore obtain a stratification of the singular set with optimal dimensional bounds depending on the symmetries of the tangent flows. Our methods also imply the corresponding quantitative stratification result and the expected $L^p$-curvature bounds.       As an application we obtain a description of the singularity formation at the first singular time and a long-time characterization of immortal flows, which generalizes the thick-thin decomposition in dimension 3. We also obtain a backwards pseudolocality theorem and discuss several other applications.

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Langue :
Anglais
Crédits
Fanny Bastien (Réalisation), Hugo BÉCHET (Réalisation)
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CC BY-NC-ND 4.0
Citer cette ressource:
I_Fourier. (2021, 29 juin). R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions. [Vidéo]. Canal-U. https://www.canal-u.tv/107565. (Consultée le 21 mai 2022)
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