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

Authors

  • Gilles Carron Nantes Université, CNRS, Laboratoire de Mathématiques Jean Leray
  • Ilaria Mondello Université Paris Est Créteil, Laboratoire d’Analyse et Mathématiques appliqués
  • David Tewodrose Vrije Universiteit Brussel, Department of Mathematics and Data Science

DOI:

https://doi.org/10.54330/afm.176490

Keywords:

Gromov–Hausdorff convergence, Ricci curvature, Kato class, rectifiability

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 \(C^\alpha\)-manifold.

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Published

2025-10-22

Issue

Vol. 50 No. 2 (2025)

Section

Articles

License

Copyright (c) 2025 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Limits of manifolds with a Kato bound on the Ricci curvature. II. (2025). Annales Fennici Mathematici, 50(2), 623–663. https://doi.org/10.54330/afm.176490