Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bakry-\'Emery Ricci Curvature Bounds on Manifolds with Boundary   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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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat