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math.AP2026
A Liouville Theorem for Domains in Graphs
Philipp Hake, Matthias Keller, Felix Pogorzelski +1
We show a Liouville theorem for domains in graphs with Dirichlet boundary conditions. More specifically, we characterize the non-existence of non-zero bounded harmonic functions. S…
math.FA2026
Graphs at infinity: Liouville theorems, Recurrence and Characterization of Dirichlet forms
Matthias Keller, Daniel Lenz, Marcel Schmidt
We survey recent results on graphs and their Laplacians related to the behavior of the graph at large. In particular, we focus on Liouville theorems, recurrence and characterizatio…