Besicovitch-Federer投影定理与Riemann surfaces上的测测地流
Besicovitch-Federer projection theorem and geodesic flows on Riemann surfaces
摘要：
本文将Besicovitch-Federer投影定理推广到横截映射族。作为应用，我们证明了在一类具有常负曲率和边界的Riemann曲面上，存在在具有二维支集的测地流下不变的自然二维测度，使得它们在基流形上的投影是二维的，但投影的支集是Lebesgue可忽略的.特别地，完全测地线的并集具有豪斯多夫维数2，并且是Lebesgue可忽略的。
英文摘要：
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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