Bakry-Émery Ricci Curvature Bounds on Manifolds with Boundary
arXiv:2110.06524
Abstract
We prove a Bakry-Émery generalization of a theorem of Petersen and Wilhelm, itself a generalization of a theorem of Frankel, that closed minimal hypersurfaces in a complete manifold with a suitable curvature bound must intersect. We then prove splitting theorems of Croke-Kleiner type for manifolds bounded by hypersurfaces obeying Bakry-Émery curvature bounds. Motivated in part by the near-horizon geometry programme of general relativity, we do not assume that the Bakry-Émery vector field is of gradient type.
New citations incorporated