Milan Journal of Mathematics

, Volume 76, Issue 1, pp 229–256

Aspects of Potential Theory on Manifolds, Linear and Non-linear

Article

Abstract.

We describe some aspects of potential theory on Riemannian manifolds, concentrating on Liouville-type theorems and their relationships with the parabolicity and stochastic completeness of the underlying manifold. Some generalizations of these concepts to the case of non-linear operators are also discussed.

Mathematics Subject Classification (2000).

Primary 31C12 Secondary 53C21, 58J05 

Keywords.

Potential theory on manifolds Liouville-type theorems parabolicity stochastic completeness p-Laplacian 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Stefano Pigola
    • 1
  • Marco Rigoli
    • 2
  • Alberto G. Setti
    • 1
  1. 1.Dipartimento di Fisica e MatematicaUniversità dell’Insubria – ComoComoItaly
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanoItaly

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