Exotic eigenvalues of shrinking metric graphs - Archive ouverte HAL
Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2024

Exotic eigenvalues of shrinking metric graphs

Valeurs propres exotiques de contractions de graphes

Gregory Berkolaiko
Yves Colin de Verdière

Résumé

Eigenvalue spectrum of the Laplacian on a metric graph with arbitrary but fixed vertex conditions is investigated in the limit as the lengths of all edges decrease to zero at the same rate. It is proved that there are exactly four possible types of eigenvalue asymptotics. The number of eigenvalues of each type is expressed via the index and nullity of a form defined in terms of the vertex conditions.

Dates et versions

hal-04701304 , version 1 (18-09-2024)

Identifiants

Citer

Gregory Berkolaiko, Yves Colin de Verdìère, Yves Colin de Verdière. Exotic eigenvalues of shrinking metric graphs. Journal of Mathematical Analysis and Applications, 2024, 534 (1), pp.128040. ⟨10.1016/j.jmaa.2023.128040⟩. ⟨hal-04701304⟩
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