论文信息 - Riemannian Center of Mass and so called karcher mean

Riemannian Center of Mass and so called karcher mean

The Riemannian center of mass was constructed in (GrKa) (1973). In (GKR1, GKR2, Gr, Ka, BuKa) (1974-1981) it was successfully applied with more refined estimates. Probably in 1990 someone renamed it without justification into karcher mean and references to the older papers were omitted by those using the new name. As a consequence newcomers started to reprove results from the above papers. - Here I explain the older history. The Euclidean center of mass is an affinenotion. I will use discrete mass points rather than mass distributions, for simpler wording. Let pi 2 R n be points of weight mi with P mi = 1 (for convenience). The center is defined, without reference to a metric, as:

H. Karcher

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[3] Karsten Grove,et al. Group actions and curvature , 1974 .

[4] Karsten Grove. Center of mass and $G$-local triviality of $G$-bundles , 1976 .

[5] H. Karcher. Riemannian center of mass and mollifier smoothing , 1977 .

[6] P. Buser,et al. Gromov's almost flat manifolds , 1981 .

[7] H. Karcher,et al. Geometrische Methoden zur Gewinnung von A-Priori-Schranken für harmonische Abbildungen , 1982 .

[8] B. Afsari. Riemannian Lp center of mass: existence, uniqueness, and convexity , 2011 .