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Theses

Aspect conforme de l'opérateur de Dirac sur une variété à bord

Abstract : In this thesis, we study the conformal aspect of the spectrum of the Dirac operator on manifolds with boundary. First, we prove some lower bounds for the first eigenvalue of the Dirac operator under two local boundary conditions using the conformal covariance of these operators. A carefully treatment of these boundary conditions leads to a classical estimation of the eigenvalues of the Dirac operator under one of the preceding boundary conditions which improves a previous result of O. Hijazi, S. Montiel and A. Roldán. In a second time, we construct a spinorial conformal invariant defined from the first eigenvalue of the Dirac operator under the generalized chiral bag boundary condition. This invariant can be seen as an analogous of the Yamabe invariant in the setting of spin geometry. A detailed study of this invariant leads to the construction of the Green function for the Dirac operator.
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https://tel.archives-ouvertes.fr/tel-01747391
Contributor : Simon Raulot <>
Submitted on : Monday, September 25, 2006 - 3:47:26 PM
Last modification on : Friday, February 26, 2021 - 3:22:17 AM
Long-term archiving on: : Thursday, September 20, 2012 - 10:55:09 AM

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  • HAL Id : tel-01747391, version 2

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Simon Raulot. Aspect conforme de l'opérateur de Dirac sur une variété à bord. Mathématiques [math]. Université Henri Poincaré - Nancy 1, 2006. Français. ⟨NNT : 2006NAN10219⟩. ⟨tel-01747391v2⟩

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