Milan Journal of Mathematics

, Volume 76, Issue 1, pp 229–256

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

Article

DOI: 10.1007/s00032-008-0084-1

Cite this article as:
Pigola, S., Rigoli, M. & Setti, A.G. Milan j. math. (2008) 76: 229. doi:10.1007/s00032-008-0084-1

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 31C12Secondary 53C21, 58J05

Keywords.

Potential theory on manifoldsLiouville-type theoremsparabolicitystochastic completenessp-Laplacian

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