Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of optimal Transport Plans for the
  Monge-Kantorovich-Problem   We prove that $c$-cyclically monotone transport plans $\pi$ optimize the
Monge-Kantorovich transportation problem under an additional measurability
condition. This measurability condition is always satisfied for finitely
valued, lower semi-continuous cost functions. In particular, this yields a
positive answer to Problem 2.25 in C. Villani's book. We emphasize that we do
not need any regularity conditions as were imposed in the previous literature.

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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con