Back
 JAMP  Vol.2 No.7 , June 2014
Some Results on Riemannean Multiple Barycenters
Mostafa Zahri*, Naji Khallaf
Show more
Abstract: A characteristic of a special case of Riemannean barycenters on the unit circle is presented. The non-uniqueness of such barycenters leads to an interesting study of the so-called multiple barycenters. In this work, we deal with a smooth one-dimensional manifold S1 only. Some theoretical and computational analysis is listed.
Keywords: Smooth Manifold, Geodesic, Barycenter of Masses, Metric Space, Multiple Barycenters
Cite this paper: Zahri, M. and Khallaf, N. (2014) Some Results on Riemannean Multiple Barycenters. Journal of Applied Mathematics and Physics, 2, 503-509. doi: 10.4236/jamp.2014.27058.
References

[1]   Le, H.L. (2004) Estimation of Riemannean Barycenters. LMSJ. Mathematics of Computation, 7.

[2]   Ruedi, F. and Ruh, E.A. (2006) Barycenter and Maximum Likelihood. Differential Geometry and Its Applications, 24, 660-669. http://dx.doi.org/10.1016/j.difgeo.2006.08.009

[3]   Machado, L., Leite, F.S. and Hupner, K. (2006) Riemannean Means as Solution of Variational Problems. LMSJ. Mathematics of Computation, 7.

[4]   Ballman, W., Gromov, M. and Schroeder, V. (1985) Manifolds of Nonpositive Curvature. Birkhauser, Boston.
http://dx.doi.org/10.1007/978-1-4684-9159-3

[5]   Kendall, W.S. (1992) The Propeller: A Counter Example to a Conjectured Criterion for the Existence of Certain Harmonic Functions. Journal of the London Mathematical Society, 46, 364-374.

[6]   Evans, L. and Gariepy, R. (1992) Measure Theory and Fine Properties of Functions. Advanced Mathematical Studies, CRC Press, Boca Raton.

[7]   Chen, B.-Y. and Jiang, S. (1995) Inequalities between Volume, Center of Mass, Circumscribed Radius, Order, and Mean Curvature. Bulletin of the Belgian Mathematical Society, 2, 75-86.

[8]   Benedetti, R. and Petronio, C. (1992) Lectures on Hyperbolic Geometry. Universitext, Springer-Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-642-58158-8

[9]   Heintze, E. and Im Hof, H.C. (1977) Geometry of Horospheres. Journal of Differential Geometry, 12, 481-491

 
 
Top