Absence of non-constant harmonic functions with ℓ^p-gradient in some semi-direct products

2014/02/13 by Antoine Gournay, Gournay, Antoine
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Group Theory (math.GR) #Nonlinear Partial Differential Equations #Probability (math.PR) #math.DG #math.GR #math.PR

paper · pdf · doi:10.48550/arxiv.1402.3126

10 pages

openalex publication_date 2014/02/13 · arxiv created 2015/12/05 · arxiv updated 2015/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To obtain groups with bounded harmonic functions (which are not hyperbolic), one of the most frequent way is to look at some semi-direct products (\eg lamplighter groups). The aim here is to show that many of these semi-direct products do not admit harmonic functions with gradient in ℓ^p, for p∈ [1,∞[.

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