Regular stars as critical points

Giorgi Khimshiashvili; Gaiane Panina; Dirk Siersma

Regular stars as critical points

Giorgi Khimshiashvili, Gaiane Panina, Dirk Siersma

Research output: Contribution to journal › Article › Academic › peer-review

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

Original language	English
Pages (from-to)	17-22
Number of pages	6
Journal	Bulletin of the Georgian National Academy of Sciences
Volume	12
Issue number	4
Publication status	Published - 1 Jan 2018

Keywords

Configuration space
Coulomb energy
Critical point
Cyclic polygon
Morse index
Oriented area
Regular polygon
Star-shape regular polygon
Winding number

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title = "Regular stars as critical points",

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",

author = "Giorgi Khimshiashvili and Gaiane Panina and Dirk Siersma",

year = "2018",

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T1 - Regular stars as critical points

AU - Khimshiashvili, Giorgi

AU - Panina, Gaiane

AU - Siersma, Dirk

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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

AB - 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

KW - Configuration space

KW - Coulomb energy

KW - Critical point

KW - Cyclic polygon

KW - Morse index

KW - Oriented area

KW - Regular polygon

KW - Star-shape regular polygon

KW - Winding number

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M3 - Article

AN - SCOPUS:85070689386

SN - 0132-1447

VL - 12

SP - 17

EP - 22

JO - Bulletin of the Georgian National Academy of Sciences

JF - Bulletin of the Georgian National Academy of Sciences

IS - 4

ER -

Regular stars as critical points

Abstract

Keywords

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