Regular stars as critical points - Khimshiashvili, Giorgi; Panina, Gaiane; Siersma, Dirk (Georgian National Academy of Sciences, 2018)
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