Absence of non-constant harmonic functions with \(\ell^p\)-gradient in some semi-direct products

DOI10.1007/s11118-016-9537-2zbMath1348.31003arXiv1402.3126OpenAlexW2962726164MaRDI QIDQ300438

Antoine Gournay

Publication date: 28 June 2016

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.3126

zbMATH Keywords

energywreath products\(\ell^p\) cohomologyharmonic functions on groups

Mathematics Subject Classification ID

Cohomology of groups (20J06) Probabilistic potential theory (60J45) Extensions, wreath products, and other compositions of groups (20E22) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (2)

Harmonic functions with finite \(p\)-energy on lamplighter graphs are constant ⋮ Linear and Nonlinear Harmonic Boundaries of Graphs; An Approach with ℓ p-Cohomology in Degree One

Cites Work

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• Harmonic functions with finite \(p\)-energy on lamplighter graphs are constant
• A new proof of Gromov’s theorem on groups of polynomial growth
• Cohomologie ℓp espaces de Besov
• Lamplighter graphs do not admit harmonic functions of finite energy
• Vanishing of ℓ^p-cohomology and transportation cost
• Polynomials and harmonic functions on discrete groups

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