REVIEW 4 cited by
Riemannian Center of Mass and so called karcher mean
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original 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.
Forward citations
Cited by 4 Pith papers
-
Geometrical Smeariness -- A new Phenomenon of Fr\'echet Means
On spheres of dimension at least two, Fréchet means can converge at rate n^{-1/6} even when data avoid the antipodal point, a 'geometrical smeariness' that is absent on the circle.
-
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 c...
-
Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds
A CLT for Fréchet means on closed Riemannian manifolds follows from Bhattacharya-Lin's omnibus theorem once the cut locus is topologically stable and avoids the measure, and the stability condition is essential.
-
On the approximation of the Riemannian barycenter
Minimizing a proven lower bound on the Riemannian distance yields a certified, logarithm-free approximation of the Riemannian barycenter, demonstrated on the Stiefel manifold.
Discussion (0). Continue with ORCID to comment.