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 Lp -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 Lp conditions on the relevant quantities.
Remarks on non-compact gradient Ricci solitons
PIGOLA, STEFANO;SETTI, ALBERTO GIULIO
2011-01-01
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 Lp -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 Lp conditions on the relevant quantities.
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