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| HAL : hal-00338175, version 1 |
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| Annales Scientifiques de l École Normale Supérieure / Annales Scientifiques de l¼École Normale Supérieure; Annales Scientifiques de l¼tcole Normale Supérieure 40, 4 (2007) 675-695 |
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| Finiteness of $\pi_1$ and geometric inequalities in almost positive Ricci curvature. |
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| Erwann Aubry 1 |
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| (2007) |
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| We show that complete $n$-manifolds whose part of Ricci curvature less than a positive number is small in $L^p$ norm (for $p>n/2$) have bounded diameter and finite fundamental group. On the contrary, complete metrics with small $L^{n/2}$-norm of the same part of the Ricci curvature are dense in the set of metrics of any compact differentiable manifold. |
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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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| Ricci curvature – comparison theorems – fundamental group |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00338175, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00338175 | |
| oai:hal.archives-ouvertes.fr:hal-00338175 | |
| Contributeur : Erwann Aubry | |
| Soumis le : Mardi 11 Novembre 2008, 20:10:20 | |
| Dernière modification le : Mercredi 12 Janvier 2011, 18:04:16 | |
