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Harmonic functions on ℝ-covered foliations

Published online by Cambridge University Press:  01 August 2009

S. FENLEY ,
R. FERES  and
K. PARWANI
S. FENLEY
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA (email: [email protected])
R. FERES
Affiliation:
Department of Mathematics, Washington University, St Louis, MO 63130, USA (email: [email protected])
K. PARWANI
Affiliation:
Department of Mathematics, Eastern Illinois University, Charleston, IL 61920, USA (email: [email protected])
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Abstract

Let (M,ℱ) be a compact codimension-one foliated manifold whose leaves are endowed with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of ℱ. If every such function is constant on leaves, we say that (M,ℱ) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. A related result for ℝ-covered foliations is also established.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 4 , August 2009 , pp. 1141 - 1161
Copyright
Copyright © Cambridge University Press 2009

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