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Extremal Areas of Polygons with Fixed Perimeter

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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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Authors and Affiliations

  1. Ilia State University, Tbilisi, Georgia

    G. Khimshiashvili

  2. St.Petersburg Department of Steklov Institute of Mathematics and St.Petersburg State University, St.Petersburg, Russia

    G. Panina

  3. Utrecht University, Utrecht, The Netherlands

    D. Siersma

Authors
  1. G. Khimshiashvili
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  2. G. Panina
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  3. D. Siersma
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Corresponding author

Correspondence to G. Khimshiashvili.

Additional information

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 481, 2019, pp. 136–145.

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Khimshiashvili, G., Panina, G. & Siersma, D. Extremal Areas of Polygons with Fixed Perimeter. J Math Sci 247, 731–737 (2020). https://doi.org/10.1007/s10958-020-04835-9

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  • DOI: https://doi.org/10.1007/s10958-020-04835-9

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