Geodesic
Géométrie, Probabilité
A note on flatness of non separable tangent cone at a barycenter
[Une note sur la platitude du cône tangeant à un barycentre]
Le Gouic, Thibaut1 
1 Massachusetts Institute of Technology, Department of Mathematics and Centrale Marseille, I2M, UMR 7373, CNRS, Aix-Marseille univ., Marseille, 13453, France
Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 489-495.

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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 T b ☆ S at its (exponential) barycenter b ☆ is a subset of a Hilbert space, without separability of the tangent cone.

Étant donné une mesure de probabilité P sur un espace d’Alexandrov S avec courbure minorée, nous prouvons que le support de la mesure poussée de P sur le cône tangent T b ☆ S à son barycentre (exponentiel) b ☆ est un sous-ensemble d’un espace de Hilbert, sans condition de séparabilité du cône tangent.

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DOI : 10.5802/crmath.66

Le Gouic, Thibaut 1

1 Massachusetts Institute of Technology, Department of Mathematics and Centrale Marseille, I2M, UMR 7373, CNRS, Aix-Marseille univ., Marseille, 13453, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {A note on flatness of non separable tangent cone at a barycenter},
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Le Gouic, Thibaut. A note on flatness of non separable tangent cone at a barycenter. Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 489-495. doi : 10.5802/crmath.66. http://geodesic.mathdoc.fr/articles/10.5802/crmath.66/

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