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Limits of manifolds with
a Kato bound on the Ricci curvature
Gilles Carron, Ilaria Mondello and David Tewodrose |
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Geometry & Topology 28 (2024) 2635–2745
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Abstract |
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We study the structure of Gromov–Hausdorff limits of sequences of Riemannian manifolds whose Ricci curvature satisfies a uniform Kato bound. We first obtain Mosco convergence of the Dirichlet energies to the Cheeger energy, and show that tangent cones of such limits satisfy the condition. Under a noncollapsing assumption, we introduce a new family of monotone quantities, which allows us to prove that tangent cones are also metric cones. We then show the existence of a well-defined stratification in terms of splittings of tangent cones. We finally prove volume convergence to the Hausdorff –measure. |
Keywords
Gromov–Hausdorff convergence, Ricci curvature, Kato class,
volume convergence
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Mathematical Subject Classification
Primary: 53C21
Secondary: 53C23, 31C25, 58J35
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References |
Publication
Received: 24 April 2021
Revised: 14 September 2022
Accepted: 10 December 2022
Published: 21 October 2024
Proposed: Tobias H Colding
Seconded: Urs Lang, Gang Tian
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Authors |
| Gilles Carron | |
| Laboratoire de Mathématiques Jean
Leray, UMR 6629 Université de Nantes Nantes France |
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| Ilaria Mondello | |
| Laboratoire d’Analyse et
Mathématiques Appliquées, UMR CNRS 8050 Université Paris Est Créteil Créteil France |
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| David Tewodrose | |
| Laboratoire de Mathématiques Jean
Leray, UMR CNRS 6629 Université de Nantes Nantes France |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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