Characterizations of p-Parabolicity on Graphs

28.11.2025, 13:30 Uhr  –  Haus 9, Raum 2.22
Forschungsseminar Diskrete Spektraltheorie

Florian Fischer

We study p-energy functionals on infinite locally summable graphs for \(p \in (1,\infty) \) and discuss that many well-known characterizations for a parabolic space are also true in this discrete, non-local and non-linear setting. Among them are an Ahlfors-type, a Kelvin-Nevanlinna-Royden-type, a Khas'minskiı-type and a Poincaré-type characterization. Some of them we will study in detail. We also illustrate some applications and describe examples of graphs which are locally summable but not locally finite. Joint work with Andrea Adriani (Rabat) and Alberto Setti (Como).