Neumann Domains on Graphs and Manifolds

Lior Alon; Ram Band; Michael Bersudsky; Sebastian Egger

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arXiv · 1805.07612

Neumann Domains on Graphs and Manifolds

Lior Alon·Ram Band·Michael Bersudsky·Sebastian Egger

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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.

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BibTeX RIS

Lior Alon, Ram Band, Michael Bersudsky, Sebastian Egger. 2018-05-19. Neumann Domains on Graphs and Manifolds. https://arxiv.org/abs/1805.07612

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