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 analytic tools we develop have close ties to integral geometry.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 29-62 |
| Number of pages | 34 |
| Journal | Journal of the European Mathematical Society |
| Volume | 23 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2021 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics
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