Metric-measure boundary and geodesic flow on Alexandrov spaces

Vitali Kapovitch, Alexander Lytchak, Anton Petrunin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 languageEnglish (US)
Pages (from-to)29-62
Number of pages34
JournalJournal of the European Mathematical Society
Issue number1
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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