|
|||||
|
|
Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces |
|
| Authors: | Risto Hovila Esa J?rvenp?? Maarit J?rvenp?? Fran?ois Ledrappier |
| Affiliation: | 1. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland 2. Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, 90014, Oulu, Finland 3. LPMA, UMR 7599, Universit?? Paris 6, 4, Place Jussieu, 75252, Paris cedex 05, France |
| 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 2D measures invariant under the geodesic flow having 2D supports such that their projections to the base manifold are 2D but the supports of the projections are Lebesgue negligible. In particular, the union of complete geodesics has Hausdorff dimension 2 and is Lebesgue negligible. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |