Metric-measure boundary and geodesic flow on Alexandrov spaces
Metric-measure boundary and geodesic flow on Alexandrov spaces
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DOI：
10.4171/jems/1006
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
V. Kapovitch;A. Lytchak;A. Petrunin
中科院分区：
文献类型：
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作者：
V. Kapovitch;A. Lytchak;A. Petrunin
我们将亚历山德罗夫空间上许多无限测地线的存在性与球体积的平均增长联系起来。我们推导出测地流的存在，并在几个重要情况下保留了刘维测度。所开发的分析工具与积分几何有着密切的联系。
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.