Positive harmonic functions on groups and covering spaces

2019/06/27 by Panagiotis Polymerakis, Polymerakis, Panagiotis · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Dermatological and Skeletal Disorders #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1906.11723

openalex publication_date 2019/06/27 · openalex created_date 2019/07/12 · openalex updated_date 2026/07/28

Abstract

We show that if p \colon M → N is a normal Riemannian covering, with N closed, and M has exponential volume growth, then there are non-constant, positive harmonic functions on M. This was conjectured by Lyons and Sullivan in \citeLS.

Citations

• Differential equations on riemannian manifolds and their geometric applications

Cited by

• On the Dirichlet Problem at Infinity and Poisson Boundary for Certain Manifolds without Conjugate Points

Related

• Every exponential group supports a positive harmonic function
• Polynomially growing harmonic functions on connected groups
• Positive harmonic functions on comb-like domains
• Harmonic functions on locally compact groups of polynomial growth
• Properties for (α,β)-harmonic functions