Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces
Classical Analysis and ODEs
2012-12-13 v2 Differential Geometry
Dynamical Systems
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.
Cite
@article{arxiv.1104.3453,
title = {Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces},
author = {Risto Hovila and Esa Järvenpää and Maarit Järvenpää and François Ledrappier},
journal= {arXiv preprint arXiv:1104.3453},
year = {2012}
}
Comments
12 pages