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arXiv · 2207.05419

Torus stability under Kato bounds on the Ricci curvature

Gilles Carron·Ilaria Mondello·David Tewodrose
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Abstract

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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Gilles Carron, Ilaria Mondello, David Tewodrose. 2022-07-12. Torus stability under Kato bounds on the Ricci curvature. https://arxiv.org/abs/2207.05419

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