Regular stars as critical points
Publication date
2018-01-01
Authors
Khimshiashvili, Giorgi
Panina, Gaiane
Siersma, D.
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Document Type
Article
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Abstract
We show that star-shaped regular planar polygons are non-degenerate critical points of certain natural functions on appropriate configuration spaces and compute their Morse indices. The main new results are concerned with the Coulomb potential of equally charged vertices on the space of n-gons with fixed perimeter
Keywords
Configuration space, Coulomb energy, Critical point, Cyclic polygon, Morse index, Oriented area, Regular polygon, Star-shape regular polygon, Winding number, General
Citation
Khimshiashvili, G, Panina, G & Siersma, D 2018, 'Regular stars as critical points', Bulletin of the Georgian National Academy of Sciences, vol. 12, no. 4, pp. 17-22.