The $L^1$ Liouville Property on Weighted manifolds

Abstract

We consider a complete noncompact smooth metric measure space $(M^n,g,e^{-f}dv)$ 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 $L^1$ norm is constant.

References in corpus (1)

• Heat Kernel on Smooth Metric Measure Spaces with Nonnegative Curvature

Cited by in corpus (2)

• Heat kernel on smooth metric measure spaces and applications
• Classification of expanding and steady Ricci solitons with integral curvature decay