Riemannian means as solutions of variational problems
Luís Machado, F. Silva Leite and Knut Hüper
Abstract: The authors of this paper formulate a variational problem on a
Riemannian manifold M whose solutions are piecewise smooth
geodesics that best fit a given data set of time labelled points
in M. By a limiting process, these solutions converge to a
single point in M, which are proved to be the Riemannian mean of
the given points for some particular Riemannian manifolds such as
Euclidean spaces, connected and compact Lie groups, and spheres.
|
