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Le problème de Yamabe avec singularités et la conjecture de Hebey-Vaugon.

Abstract : In the first part of this thesis, we study the Yamabe problem with singularities, that we can announce as follow: Given a compact Riemannian manifold (M,g), find a constant scalar curvature metric, conformal to g, when g has not necessarily the usual regularity (it can be C^1). We consider also the equivariant case (in the presence of the isometry group)}. To solve this problem, we start the study of the Yamabe type equations. We show that all the known properties in the smooth case (Yamabe problem) are still valid in our case. Under some assumptions, we prove the existence and unicity of solutions for this singular Yamabe problem .
The second part is dedicated to the Hebey-Vaugon conjecture, stated in their paper about the equivariant Yamabe problem. We prove that this conjecture is true in some other new cases, after we generalize T. Aubin's theorem.
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Contributor : Farid Madani <>
Submitted on : Monday, October 5, 2009 - 5:03:37 PM
Last modification on : Wednesday, December 9, 2020 - 3:14:36 PM
Long-term archiving on: : Tuesday, October 16, 2012 - 11:50:31 AM


  • HAL Id : tel-00422095, version 1


Farid Madani. Le problème de Yamabe avec singularités et la conjecture de Hebey-Vaugon.. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2009. Français. ⟨tel-00422095⟩



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