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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
Article

Abstract

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.

Keywords

Ricci solitons Triviality Scalar curvature Maximum principles Liouville-type theorems 

Mathematics Subject Classification (2000)

53C21 

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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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