Torus stability under Kato bounds on the Ricci curvature
Résumé
We show two stability results for a closed Riemannian manifold whose Ricci curvature is small in the Kato sense and whose first Betti number is equal to the dimension. The first one is a geometric stability result stating that such a manifold is Gromov-Hausdorff close to a flat torus. The second one states that, under a stronger assumption, such a manifold is diffeomorphic to a torus: this extends a result by Colding and Cheeger-Colding obtained in the context of a lower bound on the Ricci curvature.
Domaines
Géométrie différentielle [math.DG]
Fichier principal
Journal of London Math Soc - 2022 - Carron - Torus stability under Kato bounds on the Ricci curvature.pdf (286.71 Ko)
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