Journal of the Mathematical Society of Japan

Convex functions and barycenter on CAT(1)-spaces of small radii

Takumi YOKOTA

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Abstract

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.

Article information

Source
J. Math. Soc. Japan Volume 68, Number 3 (2016), 1297-1323.

Dates
First available in Project Euclid: 19 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1468956169

Digital Object Identifier
doi:10.2969/jmsj/06831297

Mathematical Reviews number (MathSciNet)
MR3523548

Zentralblatt MATH identifier
1351.53057

Subjects
Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

Keywords
CAT(1)-space convex function barycenter Banach–Saks property

Citation

YOKOTA, Takumi. Convex functions and barycenter on CAT(1)-spaces of small radii. J. Math. Soc. Japan 68 (2016), no. 3, 1297--1323. doi:10.2969/jmsj/06831297. https://projecteuclid.org/euclid.jmsj/1468956169.


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