Open Access
July, 2016 Convex functions and barycenter on CAT(1)-spaces of small radii
J. Math. Soc. Japan 68(3): 1297-1323 (July, 2016). DOI: 10.2969/jmsj/06831297


We use the convexity of a certain function discovered by W. Kendall on small metric balls in CAT(1)-spaces to show that any probability measure on a complete CAT(1)-space of small radius admits a unique barycenter. We also present various properties of barycenter on those spaces. This extends the results previously known for CAT(0)-spaces and CAT(1)-spaces of small diameter.


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Takumi YOKOTA. "Convex functions and barycenter on CAT(1)-spaces of small radii." J. Math. Soc. Japan 68 (3) 1297 - 1323, July, 2016.


Published: July, 2016
First available in Project Euclid: 19 July 2016

zbMATH: 1351.53057
MathSciNet: MR3523548
Digital Object Identifier: 10.2969/jmsj/06831297

Primary: 53C23

Keywords: Banach–Saks property , Barycenter , CAT(1)-space , convex function

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 3 • July, 2016
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