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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 481, Pages 136–145 (Mi znsl6783)  
This article is cited in 3 scientific papers (total in 3 papers)

Extremal areas of polygons with fixed perimeter

G. Khimshiashvilia, G. Paninabc, D. Siersmad

a Ilia State University, Tbilisi, Georgia
b St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia
c St. Petersburg State University, St. Petersburg, Russia
d Utrecht University, Utrecht, The Netherlands
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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 $\mathbb{C}P^{n-2}$. 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. Bibliography: 11 titles.
Key words and phrases: planar polygon, isoperimetric problem, configuration space, oriented area, critical point, Morse index.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00128_a
Russian Academy of Sciences - Federal Agency for Scientific Organizations 08-04
This work is supported by the RFBR grant 17-01-00128 and by the Presidium of RAS program “New Methods of Mathematical Modelling in Nonlinear Dynamical Systems” (grant 08-04).
Received: 12.07.2019
Document Type: Article
UDC: 515.164.174
Language: English
Citation: G. Khimshiashvili, G. Panina, D. Siersma, “Extremal areas of polygons with fixed perimeter”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXX, Zap. Nauchn. Sem. POMI, 481, POMI, St. Petersburg, 2019, 136–145
Citation in format AMSBIB
\Bibitem{KhiPanSie19}
\by G.~Khimshiashvili, G.~Panina, D.~Siersma
\paper Extremal areas of polygons with fixed perimeter
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XXX
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 481
\pages 136--145
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6783}
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  • https://www.mathnet.ru/eng/znsl/v481/p136
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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