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arXiv · 2110.06524

Bakry-\'Emery Ricci Curvature Bounds on Manifolds with Boundary

Kenneth Moore·Eric Woolgar
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Abstract

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.

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BibTeXRIS

Kenneth Moore, Eric Woolgar. 2021-10-13. Bakry-\'Emery Ricci Curvature Bounds on Manifolds with Boundary. https://arxiv.org/abs/2110.06524

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