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R. Perales - Recent Intrinsic Flat Convergence Theorems

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

Given a closed and oriented manifold M and Riemannian tensors g0, g1, ... on M that satisfy g0 < gj, vol(M, gj)vol (M, g0) and diam(M, gj)D we will see that (M, gj) converges to (M, g0) in the intrinsic flat sense. We also generalize this to the non-empty bundary setting. We remark that under the onditions we do not nexessarily obtain smooth, C0 or even Gromov-Hausdorff convergence. furthermore, these results can be applied to show stability of a class of tori and a class of complete and asymptotically flat manifolds. That is, any sequence of tori in the former class with almost nonnegative scalar curvature convergences to a flat tori, and any sequence of manifolds in the latter with ADM masses converging to zero converges to Euclidean space. [Based on joint work with Allen, Allen-Sormani and Cabrera Pacheco-Katterer].

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Langue :
Anglais
Crédits
Fanny Bastien (Réalisation), Hugo BÉCHET (Réalisation)
Conditions d'utilisation
CC BY-NC-ND 4.0
Citer cette ressource:
I_Fourier. (2021, 29 juin). R. Perales - Recent Intrinsic Flat Convergence Theorems. [Vidéo]. Canal-U. https://www.canal-u.tv/107563. (Consultée le 21 mai 2022)
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