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| HAL : hal-00343654, version 1 |
| arXiv : 0810.0149 |
| Fiche détaillée |  Récupérer au format |
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| International Mathematics Research Notices 2009, 10 (2009) 1933-1946 |
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| Bounds on the volume entropy and simplicial volume in Ricci curvature $L^p$ bounded from below |
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| Erwann AUBRY 1 |
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| (2009) |
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| Let $(M,g)$ be a compact manifold with Ricci curvature almost bounded from below and $\pi:\bar{M}\to M$ be a normal, Riemannian cover. We show that, for any nonnegative function $f$ on $M$, the means of $f\o\pi$ on the geodesic balls of $\bar{M}$ are comparable to the mean of $f$ on $M$. Combined with logarithmic volume estimates, this implies bounds on several topological invariants (volume entropy, simplicial volume, first Betti number and presentations of the fundamental group) in Ricci curvature $L^p$-bounded from below. |
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| 1 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] |
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| Domaine | : | Mathématiques/Géométrie différentielle |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/0810.0149 |
| hal-00343654, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00343654 | |
| oai:hal.archives-ouvertes.fr:hal-00343654 | |
| Contributeur : Erwann Aubry | |
| Soumis le : Mardi 2 Décembre 2008, 14:20:05 | |
| Dernière modification le : Mercredi 12 Janvier 2011, 17:55:40 | |
