Talk by Ram Band
On October 7th, 2020, Prof. Dr. Ram Band (Technion, Haifa) gave a talk about "Neumann domains on manifolds and graphs" as part of the research seminar Analysis of the FernUniversität in Hagen.
The nodal set of a Laplacian eigenfunction forms a partition of the underlying manifold or graph.
Another natural partition is based on the gradient vector field of the eigenfunction (on a manifold) or on the extremal points of the eigenfunction (on a graph).
The submanifolds (or subgraphs) of this partition are called Neumann domains (you may guess the reason for this name, and it will also be mentioned in the talk ;) )
We present some interesting results concerning Neumann domains on manifolds and on graphs.
We compare manifolds to graphs in this sense and also relate the Neumann domain results to the nodal domain study.
The talk is based on joint works with Lior Alon, Graham Cox, Sebastian Egger, David Fajman and Alexander Taylor.