151 citations
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math.SP2008★ 4 cited
Geometric and spectral properties of locally tessellating planar graphs
Matthias Keller, Norbert Peyerimhoff
In this article, we derive bounds for values of the global geometry of locally tessellating planar graphs, namely, the Cheeger constant and exponential growth, in terms of combinat…
math.SP2007★ 1 cited
Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains
Denis Borisov, Pedro Freitas
We consider the Laplace operator with Dirichlet boundary conditions on a planar domain and study the effect that performing a scaling in one direction has on the spectrum. We deriv…