Metric-measure boundary and geodesic flow on Alexandrov spaces
Differential Geometry
2021-02-02 v3 Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1705.04767,
title = {Metric-measure boundary and geodesic flow on Alexandrov spaces},
author = {Vitali Kapovitch and Alexander Lytchak and Anton Petrunin},
journal= {arXiv preprint arXiv:1705.04767},
year = {2021}
}