Abstract
We establish unique existence of $p$-barycenter of any probability measure for $p \ge 2$ on CAT(1)-spaces of small radii. In our proof, we employ Kendall's convex function on a ball of CAT(1)-spaces instead of the convexity of distance function. Various properties of $p$-barycenter on those spaces are also presented. They extend the author's previous work [Yo].
Citation
Takumi Yokota. "Convex functions and $p$-barycenter on CAT(1)-spaces of small radii." Tsukuba J. Math. 41 (1) 43 - 80, July 2017. https://doi.org/10.21099/tkbjm/1506353559
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