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

被引：18

作者：

Yokota, Takumi ^{[1
]}

机构：

[1] Kyoto Univ, Math Sci Res Inst, Kyoto 6068502, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2016年 / 68卷 / 03期

关键词：

CAT(1)-space; convex function; barycenter; Banach-Saks property; CENTER-OF-MASS; HARMONIC MAPS; METRIC-SPACES; ERGODIC THEOREM; CURVATURE; UNIQUENESS; EXISTENCE; VALUES;

D O I：

10.2969/jmsj/06831297

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1297 / 1323

页数：27

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