Morse index of a cyclic polygon
arXiv:1007.2740
Abstract
It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper, we announce an explicit formula of the Morse index for the signed area of a cyclic configuration. It depends not only on the combinatorics of a cyclic configuration, but also includes some metric characterization.
(corrected 03.09.2010)