Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces, Geom. Dedicata 161


ABSTRACT. We extend the Besicovitch-Federer projection theorem to transver-sal 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 hav-ing 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. 1

Similar works

Full text

oai:CiteSeerX.psu: time updated on 10/30/2017

This paper was published in CiteSeerX.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.