Discrete Curvature

Theory and Applications


A colloquium on discrete curvature

On the spectral theory of negatively curved planar graphs

Matthias Keller

Slides are available by following the link.

We give a survey about the spectral consequences of upper bounds on the curvature on planar graphs. A particular focus lies on uniformly decreasing curvature. This case is characterized by purely discrete spectrum for which we present eigenvalue asymptotics, exponential decay of eigenfunctions and absence of compactly supported eigenfunctions.

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