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math.SP2024
Torsional Rigidity on Metric Graphs with Delta-Vertex Conditions
Sedef Özcan, Matthias Täufer
We investigate the torsion function or landscape function and its integral, the torsional rigidity, of Laplacians on metric graphs subject to -vertex conditions. A variational c…
math.AP2024
Graph structure of the nodal set and bounds on the number of critical points of eigenfunctions on Riemannian manifolds
Matthias Hofmann, Matthias Täufer
In this article, we illustrate and draw connections between the geometry of zero sets of eigenfunctions, graph theory and the vanishing order of eigenfunctions. We identify the nod…
math.SP2024★ 1 cited
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…