We relate the existence of many infinite geodesics on Alexandrov spaces to a statement about the average growth of volumes of balls. We deduce that the geodesic flow exists and preserves the Liouville measure in several important cases. The developed analytic tool has close ties to integral geometry.

中文翻译：

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Alexandrov 空间上的度量边界和测地线流

我们将 Alexandrov 空间上许多无限测地线的存在与关于球体积平均增长的陈述联系起来。我们推断出测地线流存在并在几个重要情况下保留了 Liouville 测度。开发的分析工具与积分几何关系密切。