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.
|Number of pages||27|
|Journal||Journal of the Mathematical Society of Japan|
|Publication status||Published - 2016|
- Banach-Saks property.
- Convex function
ASJC Scopus subject areas