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dc.contributor.authorLampart, Jonas
dc.date.accessioned2014-12-15T09:33:28Z
dc.date.available2014-12-15T09:33:28Z
dc.date.issued2015
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14435
dc.language.isoenen
dc.subjectNodal seten
dc.subjectAdiabatic limiten
dc.subjectLaplacianen
dc.subjectFibre bundleen
dc.subject.ddc515en
dc.titleConvergence of nodal sets in the adiabatic limiten
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the nodal sets of non-degenerate eigenfunctions of the Laplacian on fibre bundles π:M→B in the adiabatic limit. This limit consists in considering a family Gε of Riemannian metrics that are close to Riemannian submersions, for which the ratio of the diameter of the fibres to that of the base is given by ε≪1 . We assume M to be compact and allow for fibres F with boundary, under the condition that the ground state eigenvalue of the Dirichlet Laplacian on Fx is independent of the base point. We prove for dim(B)≤3 that the nodal set of the Dirichlet eigenfunction φ converges to the pre-image under π of the nodal set of a function ψ on B that is determined as the solution to an effective equation. In particular, this implies that the nodal set meets the boundary for ε small enough and shows that many known results on this question obtained for some types of domains, also hold on a large class of manifolds with boundary. For the special case of a closed manifold M fibred over the circle B=S1 , we obtain finer estimates and prove that every connected component of the nodal set of φ is smoothly isotopic to the typical fibre of π:M→S1 .en
dc.relation.isversionofjnlnameAnnals of Global Analysis and Geometry
dc.relation.isversionofjnlvol47
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages147-166
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s10455-014-9440-2en
dc.identifier.urlsitehttp://arxiv.org/abs/1405.1903v2en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen


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