JournalsjemsVol. 23, No. 1pp. 29–62

Metric-measure boundary and geodesic flow on Alexandrov spaces

  • Vitali Kapovitch

    University of Toronto, Canada
  • Alexander Lytchak

    Universität Köln, Germany
  • Anton Petrunin

    University Park, USA
Metric-measure boundary and geodesic flow on Alexandrov spaces cover
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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.

Cite this article

Vitali Kapovitch, Alexander Lytchak, Anton Petrunin, Metric-measure boundary and geodesic flow on Alexandrov spaces. J. Eur. Math. Soc. 23 (2021), no. 1, pp. 29–62

DOI 10.4171/JEMS/1006