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arXiv · 1104.3453

Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces

Risto Hovila·Esa Järvenpää·Maarit Järvenpää·François Ledrappier
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Abstract

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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Risto Hovila, Esa Järvenpää, Maarit Järvenpää, François Ledrappier. 2011-04-18. Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces. https://arxiv.org/abs/1104.3453

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