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. 
Hermann Karcher
math.HO math.DG