Abstract
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.
Citation
Yoshihiro Shikata. "On geometric variation theory." Nagoya Math. J. 156 159 - 169, 1999.
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