Metric-measure boundary and geodesic flow on Alexandrov spaces

Alexander Lytchak; Anton Petrunin; Vitali Kapovitch

Metric-measure boundary and geodesic flow on Alexandrov spaces

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arxiv 1705.04767 v3 pith:ZFMUCNQD submitted 2017-05-12 math.DG math.MG

Vitali Kapovitch , Alexander Lytchak , Anton Petrunin This is my paper · ORCID

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keywords alexandrovflowgeodesicspacesanalyticaverageballsboundary

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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.

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Rectifiability of the reduced boundary for sets of finite perimeter over RCD$(K,N)$ spaces
math.MG 2019-09 conditional novelty 7.0 of 10

In RCD(K,N) spaces, the reduced boundary of a set of finite perimeter has a unique Euclidean half-space tangent at almost every point and is rectifiable by bi-Lipschitz charts.

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