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SUMMARY:The Steklov and Laplacian spectra of Riemannian manifolds with bou
 ndary
DTSTART:20181128T130000
DTEND:20181128T140000
DTSTAMP:20260916T220418Z
UID:099e91692bf3b5ad32685be002038be06086e4e38d96a1ee791a71f2
CATEGORIES:Conferences - Seminars
DESCRIPTION:Alexandre Girouard\, Professeur agrégé au Département de m
 athématiques et de statistique de l'Université Laval\, Québec\nThe Dir
 ichlet-to-Neumann map is a first order pseudodifferential operator acting 
 on the smooth functions of the boundary of a compact Riemannian manifold M
 . Its spectrum is known as the Steklov spectrum of M. The asymptotic behav
 iour (as j tends to infinity) of the Steklov eigenvalues s_j is determined
  by the Riemannian metric on the boundary of M. Neverthless\, each individ
 ual eigenvalue can become arbitrarily big if the Riemannian metric is pert
 urbed adequately. This can be achieved while keeping the geometry of the b
 oundary unchanged\, but it requires modifications of the metric in arbitra
 rily small neighborhoods of the boundary. In our recent work with Bruno Co
 lbois and Asma Hassannezhad\, we impose constraints on the geometry of M o
 n and near its boundary. This allows the comparison of each Steklov eigenv
 alue s_j with the eigenvalues l_j of the Laplace operator acting on the bo
 undary. This control is uniform in the index j. In this talk I will discus
 s the proof of this result\, which is based on the Pohozaev identity and o
 n comparison results for the principal curvatures of hypersurfaces that ar
 e parallel to the boundary.
LOCATION:MA B2 485 https://plan.epfl.ch/?room=MAB2485
STATUS:CONFIRMED
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