Spectral estimates for infinite quantum graphs

  title={Spectral estimates for infinite quantum graphs},
  author={Aleksey Kostenko and Noema Nicolussi},
  journal={Calculus of Variations and Partial Differential Equations},
We investigate the bottom of the spectra of infinite quantum graphs, i.e., Laplace operators on metric graphs having infinitely many edges and vertices. We introduce a new definition of the isoperimetric constant for quantum graphs and then prove the Cheeger-type estimate. Our definition of the isoperimetric constant is purely combinatorial and thus it establishes connections with the combinatorial isoperimetric constant, one of the central objects in spectral graph theory and in the theory of… 
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