Neumann Domains on Graphs and Manifolds
Spectral Theory
2018-05-22 v1 Mathematical Physics
math.MP
Abstract
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. This paper reviews the subject, as appears in a few recent works and points out some open questions and conjectures. The paper concerns both manifolds and metric graphs and the exposition allows for a comparison between the results obtained for each of them.
Keywords
Cite
@article{arxiv.1805.07612,
title = {Neumann Domains on Graphs and Manifolds},
author = {Lior Alon and Ram Band and Michael Bersudsky and Sebastian Egger},
journal= {arXiv preprint arXiv:1805.07612},
year = {2018}
}