Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below

We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature bounded below and diameter bounded above, Gromov-Hausdorff convergence agrees with intrinsic flat convergence. In particular, the limiting current is essentially unique, has multiplicit...

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Detalles Bibliográficos
Autores principales: Matveev, Rostislav, Portegies, Jacobus W.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2016
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6294178/
https://www.ncbi.nlm.nih.gov/pubmed/30839891
http://dx.doi.org/10.1007/s12220-016-9742-7
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author Matveev, Rostislav
Portegies, Jacobus W.
author_facet Matveev, Rostislav
Portegies, Jacobus W.
author_sort Matveev, Rostislav
collection PubMed
description We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature bounded below and diameter bounded above, Gromov-Hausdorff convergence agrees with intrinsic flat convergence. In particular, the limiting current is essentially unique, has multiplicity one, and mass equal to the Hausdorff measure. Moreover, the limit spaces satisfy a constancy theorem.
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spelling pubmed-62941782018-12-28 Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below Matveev, Rostislav Portegies, Jacobus W. J Geom Anal Article We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature bounded below and diameter bounded above, Gromov-Hausdorff convergence agrees with intrinsic flat convergence. In particular, the limiting current is essentially unique, has multiplicity one, and mass equal to the Hausdorff measure. Moreover, the limit spaces satisfy a constancy theorem. Springer US 2016-09-28 2017 /pmc/articles/PMC6294178/ /pubmed/30839891 http://dx.doi.org/10.1007/s12220-016-9742-7 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Matveev, Rostislav
Portegies, Jacobus W.
Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below
title Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below
title_full Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below
title_fullStr Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below
title_full_unstemmed Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below
title_short Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below
title_sort intrinsic flat and gromov-hausdorff convergence of manifolds with ricci curvature bounded below
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6294178/
https://www.ncbi.nlm.nih.gov/pubmed/30839891
http://dx.doi.org/10.1007/s12220-016-9742-7
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