Title: Nodal length of Steklov eigenfunctions
Speaker: David Sher
Speaker Info: DePaul
Brief Description:
Special Note:
Abstract:
Consider Steklov eigenfunctions on a surface with boundary, which are the harmonic extensions of eigenfunctions of the Dirichlet-to-Neumann map on the boundary. Motivated by analogous questions for Laplace eigenfunctions, we are interested in understanding the nodal sets (i.e. the zero sets) of these Steklov eigenfunctions. A conjecture in the spirit of Yau states that the nodal length - that is, the length of the nodal set - of a Steklov eigenfunction should be bounded above and below by a geometric constant times the associated Steklov eigenvalue. We prove this conjecture under the assumption that the surface with boundary is real analytic. I will give a detailed explanation of the background and of our theorem, then sketch the key points of the proof. This is joint work with I. Polterovich (U. de Montreal) and J. Toth (McGill).Date: Monday, October 24, 2016