A note on flatness of non separable tangent cone at a barycenter
Given a probability measure $\mathbf{P}$ on an Alexandrov space $S$ with curvature bounded below, we prove that the support of the pushforward of $\mathbf{P}$ on the tangent cone $T_{b^\star }S$ at its (exponential) barycenter $b^\star $ is a subset of a Hilbert space, without separability of the ta...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2020-07-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.66/ |
| _version_ | 1797651576283725824 |
|---|---|
| author | Le Gouic, Thibaut |
| author_facet | Le Gouic, Thibaut |
| author_sort | Le Gouic, Thibaut |
| collection | DOAJ |
| description | Given a probability measure $\mathbf{P}$ on an Alexandrov space $S$ with curvature bounded below, we prove that the support of the pushforward of $\mathbf{P}$ on the tangent cone $T_{b^\star }S$ at its (exponential) barycenter $b^\star $ is a subset of a Hilbert space, without separability of the tangent cone. |
| first_indexed | 2024-03-11T16:17:47Z |
| format | Article |
| id | doaj.art-e8a2e8f3f970403982d8d53894c66ab5 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:47Z |
| publishDate | 2020-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-e8a2e8f3f970403982d8d53894c66ab52023-10-24T14:19:02ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692020-07-01358448949510.5802/crmath.6610.5802/crmath.66A note on flatness of non separable tangent cone at a barycenterLe Gouic, Thibaut0https://orcid.org/0000-0001-6983-2794Massachusetts Institute of Technology, Department of Mathematics and Centrale Marseille, I2M, UMR 7373, CNRS, Aix-Marseille univ., Marseille, 13453, FranceGiven a probability measure $\mathbf{P}$ on an Alexandrov space $S$ with curvature bounded below, we prove that the support of the pushforward of $\mathbf{P}$ on the tangent cone $T_{b^\star }S$ at its (exponential) barycenter $b^\star $ is a subset of a Hilbert space, without separability of the tangent cone.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.66/ |
| spellingShingle | Le Gouic, Thibaut A note on flatness of non separable tangent cone at a barycenter Comptes Rendus. Mathématique |
| title | A note on flatness of non separable tangent cone at a barycenter |
| title_full | A note on flatness of non separable tangent cone at a barycenter |
| title_fullStr | A note on flatness of non separable tangent cone at a barycenter |
| title_full_unstemmed | A note on flatness of non separable tangent cone at a barycenter |
| title_short | A note on flatness of non separable tangent cone at a barycenter |
| title_sort | note on flatness of non separable tangent cone at a barycenter |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.66/ |
| work_keys_str_mv | AT legouicthibaut anoteonflatnessofnonseparabletangentconeatabarycenter AT legouicthibaut noteonflatnessofnonseparabletangentconeatabarycenter |