Morse index of a cyclic polygon. II
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A. Zhukova
Translated by: the author - St. Petersburg Math. J. 24 (2013), 461-474
- DOI: https://doi.org/10.1090/S1061-0022-2013-01247-7
- Published electronically: March 21, 2013
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Abstract:
A polygonal linkage can be imagined as a set of $n$ rigid bars connected by links cyclically. This construction lies on a plane and can rotate freely around the links, with allowed self-intersections. On the moduli space of the polygonal linkage, the signed area function $A$ is defined. G. Panina and G. Khimshiashvili proved that cyclic configurations of a polygonal linkage are the critical points of $A$. Later, G. Panina and the author described a way to compute the Morse index of a cyclic configuration of a polygonal linkage. In this paper a simple formula for the Morse index of a cyclic configuration is given. Also, a description is obtained for all possible local extrema of $A$.References
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Bibliographic Information
- A. Zhukova
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Petrodvorets, St. Petersburg 198904, Russia
- Email: millionnaya13@ya.ru
- Received by editor(s): May 29, 2011
- Published electronically: March 21, 2013
- Additional Notes: Partially supported by the program “Research in Pairs” of Mathematisches Forschungsinstitut Oberwolfach in 2010. The author thanks G. Panina, G. Khimshiashvili, and D. Siersma for their help and useful remarks
- © Copyright 2013 American Mathematical Society
- Journal: St. Petersburg Math. J. 24 (2013), 461-474
- MSC (2010): Primary 14M06; Secondary 53D30, 58E05
- DOI: https://doi.org/10.1090/S1061-0022-2013-01247-7
- MathSciNet review: 3014129