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Generalized Fermat's Problem

Published online by Cambridge University Press:  20 November 2018

R. Noda ,
T. Sakai  and
M. Morimoto
R. Noda
Affiliation:
Department of Mathematics, College of Liberal Arts and Sciences, Okayama University, Tsushima, Okayama 700, Japan
T. Sakai
Affiliation:
Department of Mathematics, Faculty of Science, Okayama University, Tsushima, Okayama 700, Japan
M. Morimoto
Affiliation:
Department of Mathematics, College of Liberal Arts and Sciences, Okayama University, Tsushima, Okayama 700, Japan
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Abstract

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The following problem is studied. Generalized Fermat's problem: in an n-dimensional Hadamard manifold M, locate a point whose distances from the given k vertices of M have the smallest possible sum.

Keywords

53A9952A20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 1 , 01 March 1991 , pp. 96 - 104
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Berger, M., Gauduchon, P. and Mazet, E., Le spectre d'une variété riemannienne. Lecture Notes in Math. 194 Springer, Berlin-Heidelberg-New York, 1971.Google Scholar
2. Ballmann, W., Gromov, M. and Schroeder, V., Manifolds of nonpositive curvature, Progress in Math. 61 (1985).Google Scholar
3. Cheeger, J. and Ebin, D. G., Comparison theorem in Riemannian geometry. North-Holland, Amsterdam- Oxford, American Elsevier, New York, 1975.Google Scholar
4. Coxeter, H. S. M., Introduction to geometry. John Wiley and Sons Inc., New York, 1965.Google Scholar
5. Hokari, S., Plane and spherical trigonometry (Japanese). Kyoritsu Shuppan, Tokyo, 1955.Google Scholar
6. Hokari, S., Izumi, S., Kondo, M. and Nagakura, T., Mathematical formulae (Japanese). Kyoritsu Shuppan, Tokyo, 1969.Google Scholar
7. Tanno, S., Differential geometry of manifolds (Japanese). Jikkyo Shuppan, Tokyo, 1976.Google Scholar