Abstract:We study perimeters of connecting cycles for concentric circles. More precisely, we are interested in characterization of those connecting cycles which are critical points of perimeter considered as a function on the product of given circles. Specifically, we aim at showing that, generically, perimeter is a Morse function on the configuration space, and computing Morse indices of critical configurations. In particular, we prove that the diametrically aligned configurations are critical and their indices can be… Show more
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