Stable weighted minimal surfaces in manifolds with nonnegative   Bakry-Emery Ricci tensor
  In this paper, we study stable weighted minimal hypersurfaces in manifolds with nonnegative Bakry-Emery Ricci curvature. We will give some geometric and topological applications. In particular, we give some partial classification of complete 3-manifolds with nonnegative Bakry-Emery Ricci curvature assuming that $f$ is bounded. 
Gang Liu
math.DG