Limits of manifolds with a Kato bound on the Ricci curvature. II - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Limits of manifolds with a Kato bound on the Ricci curvature. II

Résumé

We prove that metric measure spaces obtained as limits of closed Riemannian manifolds with Ricci curvature satisfying a uniform Kato bound are rectifiable. In the case of a non-collapsing assumption and a strong Kato bound, we additionally show that for any $\alpha \in (0,1)$ the regular part of the space lies in an open set with the structure of a $\mathcal{C}^\alpha$-manifold.

Dates et versions

hal-03669074 , version 1 (16-05-2022)

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Gilles Carron, Ilaria Mondello, David Tewodrose. Limits of manifolds with a Kato bound on the Ricci curvature. II. 2022. ⟨hal-03669074⟩
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