Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Carron - I. Mondello - D. Tewodrose

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

created by tewodrose on 03 May 2023



Inserted: 3 may 2023
Last Updated: 3 may 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.

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