English

The $L^1$ Liouville Property on Weighted manifolds

Differential Geometry 2014-02-26 v1 Analysis of PDEs

Abstract

We consider a complete noncompact smooth metric measure space (Mn,g,efdv)(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 ff-subharmonic function with bounded weighted L1L^1 norm is constant.

Keywords

Cite

@article{arxiv.1402.6170,
  title  = {The $L^1$ Liouville Property on Weighted manifolds},
  author = {Nelia Charalambous and Zhiqin Lu},
  journal= {arXiv preprint arXiv:1402.6170},
  year   = {2014}
}