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

Takumi Yokota

doi:10.2969/jmsj/06831297

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

Takumi Yokota

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1297-1323
Number of pages	27
Journal	Journal of the Mathematical Society of Japan
Volume	68
Issue number	3
DOIs	https://doi.org/10.2969/jmsj/06831297
Publication status	Published - 2016
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/06831297

Cite this

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abstract = "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.",

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PY - 2016

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AB - 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.

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KW - Barycenter

KW - CAT(1)-space

KW - Convex function

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

Abstract

Keywords

ASJC Scopus subject areas

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