Barycenters in Alexandrov spaces of curvature bounded below

By Shin-ichi Ohta. 2012

61 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/d3e15d842d9f97ff3d8baa4de9d9290d423a26a6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Thibaut Le Gouic
2. Guillaume Carlier
3. Philippe Rigollet
4. A. Ahidar-Coutrix
5. Quentin Paris
6. Martial Agueh
7. Austin J. Stromme
8. G. Peyr'e

In Astronomy and Astrophysics

1. Quentin Paris
2. Guillaume Carlier
3. Thibaut Le Gouic
4. Philippe Rigollet
5. Martial Agueh
6. Austin J. Stromme

Citations in the corpus

• Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics (2018, background): “Significant contributions have also focused on the more delicate context of spaces S with lower bounded curvature (Yokota, 2012; Ohta, 2012).”
• Barycenters in the Wasserstein Space (2011, background): “†CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, FRANCE carlier@ceremade.dauphine.fr. curved as illustrated by example 7.3.3 in the book of Ambrosio, Gigli and Savaré [1] and that much less is known on existence, uniqueness and properties of ”
• Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space (2019, methodology): “sen to be measurable whenever the tangent cone TpS is equipped with the σ-algebra SB generated by the closed balls. This observation follows from a straightforward adaptation of Lemmas 3.3 and 4.2 in [Oht12] and implies Borel-measurability of the log map if the tangent cone TpS is separable, since, ”