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Riemannian means as solutions of variational problems. (English) Zbl 1111.58010
Summary: 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.

##### MSC:
 58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable) 53C22 Geodesics in global differential geometry
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##### References:
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