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July 2017 Convex functions and $p$-barycenter on CAT(1)-spaces of small radii
Takumi Yokota
Tsukuba J. Math. 41(1): 43-80 (July 2017). DOI: 10.21099/tkbjm/1506353559

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].

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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

Information

Received: 1 August 2016; Revised: 22 March 2017; Published: July 2017
First available in Project Euclid: 25 September 2017

zbMATH: 1378.53056
MathSciNet: MR3705774
Digital Object Identifier: 10.21099/tkbjm/1506353559

Subjects:
Primary: 53C23

Rights: Copyright © 2017 University of Tsukuba, Institute of Mathematics

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Vol.41 • No. 1 • July 2017
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