Published Paper
Inserted: 3 may 2023
Last Updated: 13 nov 2025
Journal: Journal of the London Mathematical Society
Volume: 107
Number: 3
Pages: 943--972
Year: 2023
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.