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math.SP2026
Bounds on eigenvalue ratios of quantum graphs
Evans M. Harrell, James B. Kennedy, Gabriel J. Ramos
We study ratios of eigenvalues of the Laplacian on compact metric graphs. Our goals are threefold: First, we prove a sharp Ashbaugh--Benguria-type bound for the ratio of the first…
math.SP2024
Towards a theory of eigenvalue asymptotics on infinite metric graphs: the case of diagonal combs
James B. Kennedy, Delio Mugnolo, Matthias Täufer
We examine diagonal combs, a recently identified class of infinite metric graphs whose properties depend on one parameter. These graphs exhibit a fascinating regime where they poss…