Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Carron - I. Mondello - D. Tewodrose

Torus stability under Kato bounds on the Ricci curvature

created by tewodrose on 03 May 2023



Inserted: 3 may 2023
Last Updated: 3 may 2023

Year: 2022

ArXiv: 2207.05419 PDF


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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