Mathematische Zeitschrift

, Volume 268, Issue 3–4, pp 777–790 | Cite as

Remarks on non-compact gradient Ricci solitons

  • Stefano Pigola
  • Michele Rimoldi
  • Alberto G. Setti


In this paper we show how techniques coming from stochastic analysis, such as stochastic completeness (in the form of the weak maximum principle at infinity), parabolicity and L p -Liouville type results for the weighted Laplacian associated to the potential may be used to obtain triviality, rigidity results, and scalar curvature estimates for gradient Ricci solitons under L p conditions on the relevant quantities.


Ricci solitons Triviality Scalar curvature Maximum principles Liouville-type theorems 

Mathematics Subject Classification (2000)



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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Stefano Pigola
    • 1
  • Michele Rimoldi
    • 2
  • Alberto G. Setti
    • 1
  1. 1.Dipartimento di Fisica e MatematicaUniversità dell’Insubria - ComoComoItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly

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