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

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8 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1297-1323
Number of pages27
JournalJournal of the Mathematical Society of Japan
Issue number3
Publication statusPublished - 2016
Externally publishedYes


  • Banach-Saks property.
  • Barycenter
  • CAT(1)-space
  • Convex function

ASJC Scopus subject areas

  • Mathematics(all)


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