Positive harmonic functions on groups and covering spaces

We show that if p: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 [14].

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Bibliographische Detailangaben
Veröffentlicht in:	Advances in mathematics (New York. 1965) 2021-03, Vol.379, p.107552, Article 107552
1. Verfasser:	Polymerakis, Panagiotis
Format:	Artikel
Sprache:	eng
Schlagworte:	Exponential growth Finitely generated group Positive harmonic functions Riemannian covering Strong Liouville property Volume growth
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Beschreibung
Zusammenfassung:	We show that if p: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 [14].
ISSN:	0001-8708 1090-2082
DOI:	10.1016/j.aim.2020.107552