无共轭点的紧致高亏格曲面测地流的扩张密度
Density of expansivity for geodesic flows of compact higher genus surfaces without conjugate points
AI总结：
本文证明了在亏格大于1且无共轭点的紧致连通光滑曲面中，无带状区域的测地集合在单位切丛中构成稠密轨道集，推广了无焦点条件下的已知结论。
摘要：
设 $(M,g)$ 是亏格大于1且无共轭点的紧致连通 $C^{\infty}$ 曲面。我们证明无带状区域的测地集合在单位切丛中构成稠密轨道集。在无焦点假设下，此事实作为 Coudène 和 Shapira 的结果推论已知。他们证明了平坦带状区域是周期的，从而在单位切丛中构成零测度集。
英文摘要：
Let $(M,g)$ be a compact connected $C^{\infty}$ surface without conjugate points of genus greater than one. We show that set of geodesics without strips forms a dense set of orbits in the unit tangent bundle. This fact was known assuming no focal points as a consequence of a result of Coudène and Shapira. They showed that flat strips are periodic and hence form a set of zero measure in the unit tangent bundle.
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