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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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