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

Calculus of Variations and Geometric Measure Theory

G. Carron - I. Mondello - D. Tewodrose

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

created by tewodrose on 12 Jul 2022
modified on 12 Nov 2025

[BibTeX]

Published Paper

Inserted: 12 jul 2022
Last Updated: 12 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.