Chirurgie et second invariant de Yamabe

Abstract : The goal of this thesis is to study the relationships between the analytical, geometrical and topological properties of compact manifolds of dimension n greater or equal to 3 and the behavior of the eigenvalues of the Yamabe operator. We start by studying the properties of these eigenvalues : One of the most important observation is that their sign is a conformal invariant. We are interested particulary by the study of the seconf eigenvalue of the Yamabe operator and we enlight the relations between its sign and the existence of nodal solutions of the Yamabe equation. At last, we etablish a surgery formula for the second Yamabe invariant which allows to obtain a lower bond for the second Yamabe invariant under some topological hypothesis
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Safaa El Sayed. Chirurgie et second invariant de Yamabe. Mathématiques générales [math.GM]. Université de Lorraine, 2013. Français. ⟨NNT : 2013LORR0039⟩. ⟨tel-01749572⟩

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