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Processus de diffusion sur un flot de variétés riemanniennes.

Abstract : In this thesis, we create links between the properties of diffusion of the Riemannian manifold and its geometry. We embedd a family of Riemannian manifolds whose metric is time dependent, into a Hilbert space with its duffusion properties. Namely, via the eigenfunctions of the corresponding laplacian or its heat kernel. We prove that we can construct embeddings via a finite number of eigenfunctions for all families of Riemannian manifolds (M, g(t)) such that g(t) is analytic in t. If the volume of (M, g(t)) is constant, we can construct an embedding with a complete eigenfunctions basis. This embedding will be called  the G.P.S embedding. This embedding is very informative regarding this family of manifolds. Then, we construct the fundamental solution P for the non-linear heat equation acting on (M,g(t)), such that the volume (M, g(t)) is constant. Finally we give a conjecture on the asymptotic formula of P, and we prove that, if this conjecture is true, we can embed (M,g(t)) into a Hilbert space via P.
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Contributor : Hiba Abdallah Connect in order to contact the contributor
Submitted on : Tuesday, December 7, 2010 - 1:55:30 PM
Last modification on : Friday, March 25, 2022 - 11:09:51 AM
Long-term archiving on: : Monday, November 5, 2012 - 12:31:11 PM


  • HAL Id : tel-00544151, version 1



Hiba Abdallah. Processus de diffusion sur un flot de variétés riemanniennes.. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2010. Français. ⟨tel-00544151⟩



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