Barycentric discrete conformal maps between piecewise flat approximations of Riemannian surfaces converge, under fullness and local rigidity assumptions, to conformal maps, generalizing Rodin-Sullivan circle packing convergence.
Riemannian Center of Mass and so called karcher mean
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abstract
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.
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Convergence of discrete conformal mappings on surfaces
Barycentric discrete conformal maps between piecewise flat approximations of Riemannian surfaces converge, under fullness and local rigidity assumptions, to conformal maps, generalizing Rodin-Sullivan circle packing convergence.