The L¹ Liouville Property on Weighted manifolds

2014/02/25 by Charalambous, Nelia, Lu, Zhiqin
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Primary: 58J35 #Secondary: 53C21

paper · doi:10.48550/arxiv.1402.6170

Abstract

We consider a complete noncompact smooth metric measure space (Mⁿ,g,e^-f dv) and the associated drifting Laplacian. We find sufficient conditions on the geometry of the space so that every nonnegative f-subharmonic function with bounded weighted L¹ norm is constant.

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