A note on flatness of non separable tangent cone

Abstract

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.

References in corpus (1)

• Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendible geodesics