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Pleijel's theorem for sub-Riemannian Laplacians

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GST - Geometric spectral theory and applications

We are interested in the number of nodal domains of eigenfunctions of sub-Laplacians on sub-Riemannian manifolds. Specifically, we investigate 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 uniformly, 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 that of nilpotent groups. Further, we analyze in detail the case where the nilpotent group is a Heisenberg group times a Euclidean space.  The talk is based on joint work with Bernard Helffer.

This talk is part of the Isaac Newton Institute Seminar Series series.

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