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SUMMARY:Pleijel's theorem for sub-Riemannian Laplacians - Rupert Frank (Lu
 dwig-Maximilians-Universität München)
DTSTART:20260225T140000Z
DTEND:20260225T150000Z
UID:TALK242071@talks.cam.ac.uk
DESCRIPTION:We are interested in the number of nodal domains of eigenfunct
 ions of sub-Laplacians on sub-Riemannian manifolds. Specifically\, we inve
 stigate the validity of Pleijel's theorem\, which states that\, as soon as
  the dimension is strictly larger than 1\, the number of nodal domains of 
 an eigenfunction corresponding to the k-th eigenvalue is strictly (and uni
 formly\, in a certain sense) smaller than k for large k. We show how this 
 case can be reduced from the case of general sub-Riemannian manifolds to t
 hat of nilpotent groups. Further\, we analyze in detail the case where the
  nilpotent group is a Heisenberg group times a Euclidean space.&nbsp\;\nTh
 e talk is based on joint work with Bernard Helffer.
LOCATION:Seminar Room 2\, Newton Institute
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