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Harmonic functions on R-covered foliations and group actions on the circle
Ergodic Theory and Dynamical Systems (2009)
  • Sergio Fenley, Florida State University
  • Renato Feres, Washington University in St Louis
  • Kamlesh Parwani, Eastern Illinois University
Abstract

Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped 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. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established.

Keywords
  • Foliations,
  • Harmonic functions,
  • Brownian motion on manifolds
Disciplines
Publication Date
July, 2009
Citation Information
Sergio Fenley, Renato Feres and Kamlesh Parwani. "Harmonic functions on R-covered foliations and group actions on the circle" Ergodic Theory and Dynamical Systems Vol. 29 Iss. 4 (2009)
Available at: http://works.bepress.com/kamlesh_parwani/1/