Extremal Areas of Polygons with fixed Perimeter
Publication date
2020-06
Authors
Khimshiashvili, G.
Siersma, Dirk
Panina, G.
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Document Type
Article
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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.
Keywords
Taverne, Statistics and Probability, General Mathematics, Applied Mathematics
Citation
Khimshiashvili, G, Siersma, D & Panina, G 2020, 'Extremal Areas of Polygons with fixed Perimeter', Journal of Mathematical Sciences, vol. 247, no. 5, pp. 731–737. https://doi.org/10.1007/s10958-020-04835-9