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Inégalités isopérimétriques sur les graphes et applications en géométrie différentielle

Abstract : This thesis study certain global isoperimetric inequalities on metric graphs and riemannian manifolds. We first etablish for metric graphs an isoperimetric inequality between the volume entropy and the systole, and describe the geometry of the unit ball of the stable norm by combinatorial properties of the graph. Next we show that, for a Riemannian manifold (M, g) fixed of non trivial first Betti number, a large class of polytopes can appear as unit ball of the stable norm of metrics in the conformal class of g. Then we exhib an upperbound of the systolic volume of the connected sum of n copies of a manifold M that proves the sublinearity of the systolic constant as a function in n for any dimension. We finally present an inequality between the systole, the length of the systolic loop and the diameter of a simply connected riemannian manifold whose second homotopic group is non trival.
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Contributor : Florent Balacheff Connect in order to contact the contributor
Submitted on : Wednesday, October 12, 2005 - 2:57:52 PM
Last modification on : Monday, October 11, 2021 - 1:22:31 PM
Long-term archiving on: : Friday, April 2, 2010 - 11:00:18 PM


  • HAL Id : tel-00010580, version 1


Florent Balacheff. Inégalités isopérimétriques sur les graphes et applications en géométrie différentielle. Mathématiques [math]. Université Montpellier II - Sciences et Techniques du Languedoc, 2005. Français. ⟨tel-00010580⟩



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