manuscripta mathematica

, Volume 94, Issue 1, pp 95–110 | Cite as

p-harmonic functions on graphs and manifolds

  • Ilkka Holopainen
  • Paolo M. Soardi


We show that the LiouvilleD p -property is invariant under rough isometries between a Riemannian manifold of bounded geometry and a graph of bounded degree.

AMS Subject Classifications

31C12 31C20 53C20 58G03 94C15 


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Ilkka Holopainen
    • 1
  • Paolo M. Soardi
    • 2
  1. 1.Department of MathematicsUniversity of HelsinkiFinland
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanoItaly

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