IInfinite Graphs with Nonconstant Dirichlet Finite Harmonic Functions

DOI10.1137/0405029zbMath0752.31005OpenAlexW2054841976MaRDI QIDQ4018849

Wolfgang Woess, Donald I. Cartwright

Publication date: 16 January 1993

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0405029

zbMATH Keywords

infinite graphsDirichlet sumnonconstant harmonic functionsuniqueness of currents

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Planar graphs; geometric and topological aspects of graph theory (05C10) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Applications of graph theory to circuits and networks (94C15) Discrete potential theory (31C20)

Related Items (11)

An invariant for finitely presented \(\mathbb{C} G\)-modules ⋮ The generalized strong isoperimetric inequality in locally finite networks ⋮ Subharmonic functions on graphs ⋮ A discrete Gauss-Green identity for unbounded Laplace operators, and the transience of random walks ⋮ A Hilbert space approach to effective resistance metric ⋮ Rough Isometries and Dirichlet Finite Harmonic Functions on Graphs ⋮ Lamplighter graphs do not admit harmonic functions of finite energy ⋮ Convergence of metric graphs and energy forms ⋮ Distributional limits for the symmetric exclusion process ⋮ Recurrence and transience of the edge graph of a tiling of the Euclidean plane ⋮ Morphisms and currents in infinite nonlinear resistive networks

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