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Given a probability measure P on an Alexandrov space S with curvature bounded below, we prove that the support of the pushforward of P on the tangent cone at its (exponential) barycenter is a subset of a Hilbert space, without separability of the tangent cone.
“Alexandrov geometry: preliminary version no. 1” arXiv: 1903.08539, 2019
Stephanie Alexander, Vitali Kapovitch and Anton Petrunin · 1903
Earlier work this paper cites.
“Kirszbraun’s Theorem and Metric Spaces of Bounded Curvature”
U. Lang and V. Schroeder · 1997
Earlier work this paper cites.
“Metric spaces of lower bounded curvature”
K.. Sturm · 1999
Earlier work this paper cites.
“On tangent cones of Alexandrov spaces with curvature bounded below”
Stephanie Halbeisen · 2000
Cited alongside, same era.
“A course in metric geometry”
Dmitri Burago, Yuri Burago and Sergei Ivanov · 2001
Cited alongside, same era.
“A rigidity theorem in Alexandrov spaces with lower curvature bound”
T. Yokota · 2012
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Adil Ahidar-Coutrix, Thibaut Le and Quentin Paris · 2018
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