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Theses

Propriétés de concavité du profil isopérimétrique et applications

Abstract : We show that powers of the isoperimetric profile of a closed Riemannian manifold satisfy a family of second order differential inequalities which only depend on its dimension and on a lower bound on the Ricci curvature. Differential concavity properties on the profile, topological restrictions on minimizing regions and comparison theorems arise from these inequalities. For instance, we provide a new proof of Lévy-Gromov inequality. Moreover, most of the previous results can be extended to a more general setting : we endow a Riemannian manifold with its Riemannian distance and with a measure that has a smooth positive density with respect to the Riemannian measure. In this context, we substitute a curvature-dimension assumption for the usual lower bound on the Ricci curvature. Finally, we investigate continuity properties of the isoperimetric profiles associated to a family of closed manifolds that converge towards a closed manifold with respect to Gromov-Hausdorff topology.
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https://tel.archives-ouvertes.fr/tel-00004317
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Submitted on : Thursday, October 14, 2004 - 8:54:30 AM
Last modification on : Wednesday, November 4, 2020 - 2:05:33 PM
Long-term archiving on: : Wednesday, November 23, 2016 - 5:19:36 PM

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  • HAL Id : tel-00004317, version 2

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Vincent Bayle. Propriétés de concavité du profil isopérimétrique et applications. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2003. Français. ⟨tel-00004317v2⟩

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