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.
Metric-measure boundary and geodesic flow on Alexandrov spaces
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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 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
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.