  We prove a Bakry-\'Emery 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-\'Emery curvature bounds. Motivated in
part by the near-horizon geometry programme of general relativity, we do not
assume that the Bakry-\'Emery vector field is of gradient type.
