Skip to Main content Skip to Navigation
Theses

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.
Document type :
Theses
Complete list of metadatas

https://tel.archives-ouvertes.fr/tel-00544151
Contributor : Hiba Abdallah <>
Submitted on : Tuesday, December 7, 2010 - 1:55:30 PM
Last modification on : Wednesday, November 4, 2020 - 2:12:13 PM
Long-term archiving on: : Monday, November 5, 2012 - 12:31:11 PM

Identifiers

  • HAL Id : tel-00544151, version 1

Collections

Citation

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

Share

Metrics

Record views

988

Files downloads

290