Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetric Bounds on Convex Manifolds   We extend several Cheeger-type isoperimetric bounds for convex sets in
Euclidean space, due to Bobkov and Kannan-Lov\'asz-Simonovits, to Riemannian
manifolds having non-negative Ricci curvature. In order to extend Bobkov's
bound, we require in addition an upper bound on the sectional curvature of the
space, which permits us to use comparison tools in Cartan-Alexandrov-Toponogov
(or CAT) spaces. Along the way, we also quantitatively improve our previous
result that weak concentration assumptions imply a Cheeger-type isoperimetric
bound, to a sharp bound with respect to all parameters.

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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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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: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph