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On geometric variation theory

Published online by Cambridge University Press:  22 January 2016

Yoshihiro Shikata
Yoshihiro Shikata*
Affiliation:
Department of Mathematics, Meijo University, Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan, shikat@meijo-u.ac.jp
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Abstract

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We construct here a framework for a geometric variation of 1 dimensional geometric figures regarding them as sets of ordered points. In this framework, we can make full use of cut and paste technique to find a way to go down to the geometric smallest figure, including the topological change of the parameter space. Therefore we can discuss practical problems like switching of current flows and the minimal networks not only multiple closed geodesics.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 156 , 1999 , pp. 159 - 169
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

[K] Klingenberg, W., Lectures on closed geodesics, Springer-Verlag, 1978.Google Scholar
[ST] Seifert, H. and Threlfall, W., Variationsrechnung im Grossen, Leipzig: Teubner, 1938.Google Scholar
[W] Whitney, H., Geometric integration theory, Princeton University Press, 1956.Google Scholar