Stable weighted minimal surfaces in manifolds with non-negative Bakry-Emery Ricci tensor

Abstract

In this paper, we study stable weighted minimal hypersurfaces in manifolds with non-negative Bakry-Emery Ricci curvature. We will give some geometric and topological applications. In particular, we give some partial classification of complete 3-manifolds with non-negative Bakry-Emery Ricci curvature assuming that f is bounded.