Technion - Israel Institute of Technology Department of Mathematics ============================================ PDE AND APPLIED MATHEMATICS SEMINAR ============================================ DATE: Tuesday, January 11, 2011 SPEAKER: Dan Mangoubi, HUJI PLACE: Room 814, Amado Mathematics Building, Technion TIME: 14:30 Title: Convexity in eigenfunctions on Riemannian manifolds. Abstract: We consider eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold. In 1988 Donnelly and Fefferman proved that the order of a zero of an eigenfunction with eigenvalue t is at most t^{1/2}. This fact became one of the most important tools in the study of eigenfunctions today. The proof of Donnelly and Fefferman is based on Carleman type estimates for eigenfunctions. Later, F.-H. Lin found a simpler proof based on a variational principle. A second simplification was obtained be Jerison-Lebeau which uses standard Carleman type estimates for harmonic functions. We plan to present a proof which is based on convexity arguments in the spirit of Agmon's ideas. For further info: Gershon Wolansky, <gershonw@math.technion.ac.il> For past and future Applied Math/PDE seminars: <http://www.math.technion.ac.il/pde/seminar.html> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Gershon Wolansky <gershonw@math.technion.ac.il>