Nodal geometry of Steklov eigenfunctions

04/08/2016 - 13:30
04/08/2016 - 14:30
Jiuyi Zhu, Johns Hopkins University
McGill, Burnside Hall, 805 Sherbrooke Str West, Room 920

 The eigenvalue and eigenfunction problem is fundamental and essential in mathematical analysis. The Steklov problem is an eigenvalue problem with spectrum at the boundary of a compact Riemannian manifold. Recently the study of Steklov eigenfunctions has been attracting much attention. We obtain the sharp doubling inequality for Steklov eigenfunctions on the boundary and interior of manifolds using delicate Carleman estimates. As an application, the optimal vanishing order is derived, which describes quantitative behavior of strong unique continuation property. We can ask Yau's type conjecture for the Hausdorff measure of nodal sets of Steklov eigenfunctions on the boundary and interior of the manifold. I will describe some recent progress about this challenging direction.

Part of work is joint with C. Sogge and X. Wang.

Last edited by on Thu, 03/31/2016 - 15:37