It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.
@article{bwmeta1.element.doi-10_2478_s11533-011-0011-5,
author = {Gaiane Panina and Alena Zhukova},
title = {Morse index of a cyclic polygon},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {364-377},
zbl = {1242.52018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0011-5}
}
Gaiane Panina; Alena Zhukova. Morse index of a cyclic polygon. Open Mathematics, Tome 9 (2011) pp. 364-377. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0011-5/
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