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

Abstract

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.

14 pages, more references added

References in corpus (1)

• Eigenvalue estimate and compactness for closed $f$-minimal surfaces

Cited by in corpus (1)

• Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities