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 …

In order to become worldly things, that is, deeds and facts and events and patterns of
thoughts or ideas,[action, speech, and thought] must first be seen, heard, and remembered …

In this paper, we first prove some propositions of Sobolev spaces defined on a locally finite
graph G=(V, E), which are fundamental when dealing with equations on graphs under the …

Discrete time random walks on a finite set naturally translate via a one-to-one
correspondence to discrete Laplace operators. Typically, Ollivier curvature has been …

We prove pointwise gradient bounds for heat semigroups associated to general (possibly
unbounded) Laplacians on infinite graphs satisfying the curvature dimension condition CD …

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 …

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 …

We study solutions of the generalized porous medium equation on infinite graphs. For
nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild …

We investigate the validity of the Liouville property for a class of elliptic equations with a
potential, posed on infinite graphs. Under suitable assumptions on the graph and on the …

We propose a general condition, to ensure essential self-adjointness for the Gauss-Bonnet
operator D= d+ δ D= d+ δ, based on a notion of completeness as Chernoff. This gives …