The present book deals with the spectral geometry of infinite graphs. This topic involves the
interplay of three different subjects: geometry, the spectral theory of Laplacians and the heat …

We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on
weighted graphs. We first show that, for locally finite graphs and a certain family of metrics …

We present a study of what may be called an intrinsic metric for a general regular Dirichlet
form. For such forms we then prove a Rademacher type theorem. For strongly local forms we …

For a given subcritical discrete Schrödinger operator H on a weighted infinite graph X, we
construct a Hardy-weight w which is optimal in the following sense. The operator H− λ w is …

We investigate quantum graphs with infinitely many vertices and edges without the common
restriction on the geometry of the underlying metric graph that there is a positive lower …

A few years ago various disparities for Laplacians on graphs and manifolds were
discovered. The corresponding results are mostly related to volume growth in the context of …

Criticality theory on graphs Page 1 J. Spectr. Theory 10 (2020), 73–114 DOI 10.4171/JST/286
Journal of Spectral Theory © European Mathematical Society Criticality theory for Schrödinger …

Cheeger inequalities for unbounded graph Laplacians Page 1 DOI 10.4171/JEMS/503 J. Eur.
Math. Soc. 17, 259–271 c European Mathematical Society 2015 Frank Bauer · Matthias Keller …

We investigate the bottom of the spectra of infinite quantum graphs, ie, Laplace operators on
metric graphs having infinitely many edges and vertices. We introduce a new definition of …

We consider weighted graphs with an infinite set of vertices. We show that boundedness of
all functions of finite energy can be seen as a notion of 'relative compactness' for such …