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

共 50 条

[41] Restricted Weak Upper Semi-continuity of Subdifferentials of Convex Functions on Banach Spaces [J].

Xi Yin Zheng ;

Kung Fu Ng .

Set-Valued Analysis, 2008, 16 :245-255

[42] Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains [J].

Abanin, A. V. ;

Ishimura, R. ;

Khoi, Le Hai .

BULLETIN DES SCIENCES MATHEMATIQUES, 2012, 136 (01) :96-110

[43] Restricted weak upper semi-continuity of subdifferentials of convex functions on Banach spaces [J].

Zheng, Xi Yin ;

Ng, Kung Fu .

SET-VALUED ANALYSIS, 2008, 16 (2-3) :245-255

[44] Measure of Non-Radon-Nikodym property and differentiability of convex functions on banach spaces [J].

Zheng, XY .

SET-VALUED ANALYSIS, 2005, 13 (02) :181-196

[45] Measure of Non-Radon–Nikodym Property and Differentiability of Convex Functions on Banach Spaces [J].

Xi Yin Zheng .

Set-Valued Analysis, 2005, 13 :181-196

[46] Operator Popoviciu's inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces [J].

Alomari, Mohammad W. .

ADVANCES IN PURE AND APPLIED MATHEMATICS, 2019, 10 (04) :313-324

[47] Regularity of harmonic maps from polyhedra to CAT(1) spaces [J].

Breiner, Christine ;

Fraser, Ailana ;

Huang, Lan-Hsuan ;

Mese, Chikako ;

Sargent, Pam ;

Zhang, Yingying .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (01)

[48] CONVEX FUNCTIONS ON SYMMETRIC SPACES, SIDE LENGTHS OF POLYGONS AND THE STABILITY INEQUALITIES FOR WEIGHTED CONFIGURATIONS AT INFINITY [J].

Kapovich, Michael ;

Leeb, Bernhard ;

Millson, John .

JOURNAL OF DIFFERENTIAL GEOMETRY, 2009, 81 (02) :297-354

[49] Second derivatives of convex functions in the sense of A. D. Aleksandrov on infinite-dimensional spaces with measure [J].

Bogachev, VI ;

Goldys, B .

MATHEMATICAL NOTES, 2006, 79 (3-4) :454-467

[50] Second derivatives of convex functions in the sense of A. D. Aleksandrov on infinite-dimensional spaces with measure [J].

V. I. Bogachev ;

B. Goldys .

Mathematical Notes, 2006, 79 :454-467

← 1 2 3 4 5 →