Technion - Israel Institute of Technology
 
Department of Mathematics
 
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                                    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>
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Gershon Wolansky   <gershonw@math.technion.ac.il>