Extremal Areas of Polygons with fixed Perimeter

G. Khimshiashvili; D. Siersma; G. Panina

doi:10.1007/s10958-020-04835-9

Extremal Areas of Polygons with fixed Perimeter

G. Khimshiashvili^*, D. Siersma, G. Panina

^*Corresponding author for this work

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

Abstract

We consider the configuration space of planar n-gons with fixed perimeter, which is diffeomorphic to the complex projective space ℂPn−2. The oriented area function has the minimum number of critical points on the configuration space. We describe its critical points (these are regular stars) and compute their indices when they are Morse.

Original language	English
Pages (from-to)	731–737
Number of pages	7
Journal	Journal of Mathematical Sciences
Volume	247
Issue number	5
DOIs	https://doi.org/10.1007/s10958-020-04835-9
Publication status	Published - Jun 2020

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title = "Extremal Areas of Polygons with fixed Perimeter",

abstract = "We consider the configuration space of planar n-gons with fixed perimeter, which is diffeomorphic to the complex projective space ℂPn−2. The oriented area function has the minimum number of critical points on the configuration space. We describe its critical points (these are regular stars) and compute their indices when they are Morse.",

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AU - Siersma, D.

AU - Panina, G.

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AB - We consider the configuration space of planar n-gons with fixed perimeter, which is diffeomorphic to the complex projective space ℂPn−2. The oriented area function has the minimum number of critical points on the configuration space. We describe its critical points (these are regular stars) and compute their indices when they are Morse.

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Extremal Areas of Polygons with fixed Perimeter

Abstract

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