Ram Band, Technion

Abstract: The nodal set of a Laplacian eigenfunction forms a partition of the underlying manifold. Another natural partition is based on the gradient vector field of the eigenfunction. Explicitly, we take all the gradient flow lines which are connected to saddle points of the eigenfunction. These lines partition the manifold to submanifolds which are called Neumann domains (you may try to guess the reason for this name, or wait for the talk ;) We present some results obtained so far for Neumann domains - their count, geometric properties and spectral position. We also compare the Neumann domain results to the analogous ones within the nodal domain study.

The talk is based on joint works with Philippe Charron, Graham Cox, Sebastian Egger, David Fajman and Alexander Taylor.