Metric-measure boundary and geodesic flow on Alexandrov spaces

Vitali Kapovitch; Alexander Lytchak; Anton Petrunin

doi:10.4171/JEMS/1006

Metric-measure boundary and geodesic flow on Alexandrov spaces

Vitali Kapovitch, Alexander Lytchak, Anton Petrunin

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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	https://doi.org/10.4171/JEMS/1006
State	Published - 2021

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.4171/JEMS/1006

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title = "Metric-measure boundary and geodesic flow on Alexandrov spaces",

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.",

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AU - Lytchak, Alexander

AU - Petrunin, Anton

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PY - 2021

Y1 - 2021

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Metric-measure boundary and geodesic flow on Alexandrov spaces

Abstract

All Science Journal Classification (ASJC) codes

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