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Sur l'effondrement à l'infini des variétés asymptotiquement plates.

Abstract : This PhD thesis deals with the asymptotic geometry of complete non compact Riemannian manifolds with fast curvature decay at infinity. In order to supplement previous works, it concentrates on the case where the volume growth is non maximal, namely strictly slower than in the Euclidean space of the corresponding dimension. First, a weighted Sobolev inequality and a Hardy inequality are proved, leading to numerous generalizations of well known facts in the maximal volume growth setting. In particular, rigidity and topology finiteness theorems are proved for asymptotically flat Ricci flat manifolds. In a second part, the asymptotic structure of gravitational instantons is investigated : the main theorem asserts a gravitational instanton with cubic volume growth has the asymptotic geometry of a circle fibration over an asymptotically locally Euclidean manifold.
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Contributor : Vincent Minerbe <>
Submitted on : Tuesday, December 11, 2007 - 5:49:00 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Monday, April 12, 2010 - 6:59:21 AM


  • HAL Id : tel-00195953, version 1



Vincent Minerbe. Sur l'effondrement à l'infini des variétés asymptotiquement plates.. Mathématiques [math]. Université de Nantes, 2007. Français. ⟨tel-00195953⟩



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