27 citations · 166 across the 39 of their papers we have counts for
8 papers · 1 filter
On the uniqueness class, stochastic completeness and volume growth for graphs
Xueping Huang, Matthias Keller, Marcel Schmidt
In this note we prove an optimal volume growth condition for stochastic completeness of graphs under very mild assumptions. This is realized by proving a uniqueness class criterion…
A discrete Hopf-Rinow-theorem
Matthias Keller, Florentin Münch
We prove a version of the Hopf-Rinow-theorem with respect to path metrics on discrete spaces. The novel aspect is that we do not a priori assume local finiteness but isolate a loca…
Geometric and spectral consequences of curvature bounds on tessellations
Matthias Keller
This is a chapter of a forthcoming Lecture Notes in Mathematics "Modern Approaches to Discrete Curvature" edited by L. Najman and P. Romon. It provides a survey on geometric and sp…
Sectional curvature of polygonal complexes with planar substructures
Matthias Keller, Norbert Peyerimhoff, Felix Pogorzelski
In this paper we introduce a class of polygonal complexes for which we can define a notion of sectional combinatorial curvature. These complexes can be viewed as generalizations of…
Intrinsic metrics on graphs: A survey
Matthias Keller
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 unbounde…
Graphs of finite measure
Agelos Georgakopoulos, Sebastian Haeseler, Matthias Keller +2
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…