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

Kirjoittajat

  • 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

Avainsanat:

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

Abstrakti

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.

Tiedostolataukset

Julkaistu

2025-10-22

Numero

Vol 50 Nro 2 (2025)

Osasto

Articles

Lisenssi

Copyright (c) 2025 Annales Fennici Mathematici

Creative Commons License

Tämä työ on lisensoitu Creative Commons Nimeä-EiKaupallinen 4.0 Kansainvälinen Julkinen -lisenssillä.

Viittaaminen

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