Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Besicovitch-Federer projection theorem and geodesic flows on Riemann
  surfaces   We extend the Besicovitch-Federer projection theorem to transversal families
of mappings. As an application we show that on a certain class of Riemann
surfaces with constant negative curvature and with boundary, there exist
natural 2-dimensional measures invariant under the geodesic flow having
2-dimensional supports such that their projections to the base manifold are
2-dimensional but the supports of the projections are Lebesgue negligible. In
particular, the union of complete geodesics has Hausdorff dimension 2 and is
Lebesgue negligible.

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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom