Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces

Details Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces

2011-04-18

arxiv.org/abs/1104.3453v1

Mathematics

Classical Analysis and ODEs

12 pages

Scientific paper

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.

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