Published Paper
Inserted: 3 may 2023
Last Updated: 13 nov 2025
Journal: Annales Fennici Mathematici
Volume: 50
Number: 2
Pages: 623–663
Year: 2025
Abstract:
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.