An overview of curvature bounds and spectral theory of planar tessellations

Matthias Keller[1]

  • [1] Mathematisches Institut Friedrich Schiller Universität Jena 07743 Jena, Germany

Actes des rencontres du CIRM (2013)

  • Volume: 3, Issue: 1, page 61-68
  • ISSN: 2105-0597

Abstract

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We give a survey about the spectral consequences of upper bounds on the curvature on planar tessellating graphs. We first discuss spectral bounds and then put a particular focus on uniformly decreasing curvature. This case is characterized by purely discrete spectrum and we further present eigenvalue asymptotics and exponential decay of eigenfunctions. We then discuss absence of compactly supported eigenfunctions and dependence of the spectrum of the Laplacian on the underlying ℓ p space.

How to cite

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Keller, Matthias. "An overview of curvature bounds and spectral theory of planar tessellations." Actes des rencontres du CIRM 3.1 (2013): 61-68. <http://eudml.org/doc/275368>.

@article{Keller2013,
abstract = {We give a survey about the spectral consequences of upper bounds on the curvature on planar tessellating graphs. We first discuss spectral bounds and then put a particular focus on uniformly decreasing curvature. This case is characterized by purely discrete spectrum and we further present eigenvalue asymptotics and exponential decay of eigenfunctions. We then discuss absence of compactly supported eigenfunctions and dependence of the spectrum of the Laplacian on the underlying $\ell ^\{p\}$ space.},
affiliation = {Mathematisches Institut Friedrich Schiller Universität Jena 07743 Jena, Germany},
author = {Keller, Matthias},
journal = {Actes des rencontres du CIRM},
language = {eng},
month = {11},
number = {1},
pages = {61-68},
publisher = {CIRM},
title = {An overview of curvature bounds and spectral theory of planar tessellations},
url = {http://eudml.org/doc/275368},
volume = {3},
year = {2013},
}

TY - JOUR
AU - Keller, Matthias
TI - An overview of curvature bounds and spectral theory of planar tessellations
JO - Actes des rencontres du CIRM
DA - 2013/11//
PB - CIRM
VL - 3
IS - 1
SP - 61
EP - 68
AB - We give a survey about the spectral consequences of upper bounds on the curvature on planar tessellating graphs. We first discuss spectral bounds and then put a particular focus on uniformly decreasing curvature. This case is characterized by purely discrete spectrum and we further present eigenvalue asymptotics and exponential decay of eigenfunctions. We then discuss absence of compactly supported eigenfunctions and dependence of the spectrum of the Laplacian on the underlying $\ell ^{p}$ space.
LA - eng
UR - http://eudml.org/doc/275368
ER -

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