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math.SP2020
A theory of spectral partitions of metric graphs
James B. Kennedy, Pavel Kurasov, Corentin Léna +1
We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus…
math.SP2020
Concrete method for recovering the Euler characteristic of quantum graphs
Corentin Léna, Andrea Serio
Trace formulas play a central role in the study of spectral geometry and in particular of quantum graphs. The basis of our work is the result by Kurasov which links the Euler chara…
math.SP2019
On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains--with some numerics--
Bernard Helffer, Thomas Hoffmann-Ostenhof, François Jauberteau +1
We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in R2 for which the second eigenvalue of the D…