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Theses

Spectres asymptotiques des nilvariétés graduées

Abstract : Take a graded nilmanifold with a Riemannian (resp. Sub-Riemannian) metric. Lift the metric on its universal cover, one gets a distance which in turn yields balls. On these balls one can look at the Laplacian (resp. a Sub-Laplacian). If one focuses on the spectrum for the Dirichlet problem one can describe the asymptotic behaviour of the eigenvalues when the radius of the balls goes to infinity, using the tools of homogenisation. This also allows us to give a lower bound on the asymptotic volume of balls in terms of the volume of the Albanese Torus. In the particular case of Tori we also study the Neumann problem and we characterise the flat metrics looking at the asymptotic of the first eigenvalue for the Dirichlet case. We also investigate the situation in the Heisenberg groups.
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Submitted on : Thursday, January 10, 2002 - 3:30:27 PM
Last modification on : Wednesday, November 4, 2020 - 1:57:19 PM
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Constantin Vernicos. Spectres asymptotiques des nilvariétés graduées. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2001. Français. ⟨tel-00000950⟩

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