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The essential spectrum of the Laplacian on rapidly branching tessellations

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In this paper, we characterize absence of the essential spectrum of the Laplacian under a hyperbolicity assumption for general graphs. Moreover, we present a characterization for absence of the essential spectrum for planar tessellations in terms of curvature.

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  1. Mathematical Institute, FSU Jena, 07743, Jena, Germany

    Matthias Keller

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  1. Matthias Keller
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Correspondence to Matthias Keller.

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Keller, M. The essential spectrum of the Laplacian on rapidly branching tessellations. Math. Ann. 346, 51–66 (2010). https://doi.org/10.1007/s00208-009-0384-y

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  • DOI: https://doi.org/10.1007/s00208-009-0384-y

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