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 Mar 2023


Submitted Paper

Inserted: 12 jul 2022
Last Updated: 12 mar 2023

Year: 2022

ArXiv: 2205.01956 PDF


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.