Mathematische Zeitschrift

, Volume 268, Issue 3, pp 871–886

Cheeger constants, growth and spectrum of locally tessellating planar graphs


DOI: 10.1007/s00209-010-0699-0

Cite this article as:
Keller, M. & Peyerimhoff, N. Math. Z. (2011) 268: 871. doi:10.1007/s00209-010-0699-0


In this article, we study relations between the local geometry of planar graphs (combinatorial curvature) and global geometric invariants, namely the Cheeger constants and the exponential growth. We also discuss spectral applications.

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Mathematical InstituteFriedrich-Schiller-University JenaJenaGermany
  2. 2.Department of Mathematical SciencesUniversity of DurhamDurhamUK