Metric-measure boundary and geodesic flow on Alexandrov spaces

12 May 2017 · Vitali Kapovitch, Alexander Lytchak, Anton Petrunin ·

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.