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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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1615-7168
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Volume 14, Issue 4 (Oct 2012)

Issues

Barycenters in Alexandrov spaces of curvature bounded below

Shin-Ichi Ohta
Published Online: 2012-12-11 | DOI: https://doi.org/10.1515/advgeom-2011-058

Abstract

We investigate barycenters of probability measures on proper Alexandrov spaces of curvature bounded below, and show that they enjoy several properties relevant to or different from those in metric spaces of curvature bounded above. We prove the reverse variance inequality, and show that the push forward of a measure to the tangent cone at its barycenter has the flat support.

Keywords: Barycenter; Alexandrov space; variance inequality; Wasserstein space.

About the article

Supported in part by the Grant-in-Aid for Young Scientists (B) 20740036


Published Online: 2012-12-11

Published in Print: 2012-10-01


Citation Information: , ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2011-058.

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© 2012 by Walter de Gruyter GmbH & Co.. Copyright Clearance Center

Citing Articles

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[1]
H. Le and D. Barden
Bulletin of the London Mathematical Society, 2014, Volume 46, Number 4, Page 698
[2]
Brendan Pass
Journal of Functional Analysis, 2013, Volume 264, Number 4, Page 947

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