Torus stability under Kato bounds on the Ricci curvature
Differential Geometry
2022-10-10 v2
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.
Keywords
Cite
@article{arxiv.2207.05419,
title = {Torus stability under Kato bounds on the Ricci curvature},
author = {Gilles Carron and Ilaria Mondello and David Tewodrose},
journal= {arXiv preprint arXiv:2207.05419},
year = {2022}
}
Comments
24 pages. Comments are welcome!