On the strong Liouville property of covering spaces

DOI10.1007/s11118-022-10019-8OpenAlexW4283067716MaRDI QIDQ6072428

Panagiotis Polymerakis

Publication date: 13 October 2023

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

Full work available at URL: https://doi.org/10.1007/s11118-022-10019-8

zbMATH Keywords

exponential volume growthpositive harmonic functionsstrong Liouville propertyRiemannian coverings

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Diffusion processes and stochastic analysis on manifolds (58J65) Differential geometric aspects of harmonic maps (53C43) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Potential theory on Riemannian manifolds and other spaces (31C12)

Cites Work

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• Function theory, random paths and covering spaces
• Existence of positive harmonic functions on groups and on covering manifolds
• Related aspects of positivity in Riemannian geometry
• Equivariant discretizations of diffusions, random walks, and harmonic functions
• Positive harmonic functions on groups and covering spaces
• Asymptotic entropy and Green speed for random walks on countable groups
• A note on curvature and fundamental group
• Boundary behavior for groups of subexponential growth.
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• On the strong liouville property for co-compact Riemannian covers

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