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Article Dans Une Revue Journal of the London Mathematical Society Année : 2022

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.
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hal-03875574 , version 1 (24-05-2024)

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Gilles Carron, Ilaria Mondello, David Tewodrose. Torus stability under Kato bounds on the Ricci curvature. Journal of the London Mathematical Society, 2022, 107 (3), pp.943-972. ⟨10.1112/jlms.12704⟩. ⟨hal-03875574⟩
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