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math.FA2025
Nonlinear resistance forms
Simon Puchert, Marcel Schmidt
In this paper we introduce the notion of nonlinear resistance forms. We define a -parameter family of nonlinear resistance metrics and show their additivity over serial circuits…
math.FA2025
Nonlinear Beurling-Deny criteria
Simon Puchert
This short note introduces a simple symmetric contraction property for functionals. This property clearly characterizes Dirichlet forms in the linear case. We show that it also cha…
math.FA2023
Recurrent and (strongly) resolvable graphs
Daniel Lenz, Simon Puchert, Marcel Schmidt
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric…