• Corpus ID: 117115291

Extremal polygons in R^3

@article{Panina2012ExtremalPI,
  title={Extremal polygons in R^3},
  author={Gaiane Panina},
  journal={arXiv: Geometric Topology},
  year={2012}
}
  • G. Panina
  • Published 2 January 2012
  • Mathematics
  • arXiv: Geometric Topology
The oriented area function $A$ is (generically) a Morse function on the space of planar configurations of a polygonal linkage. We are lucky to have an easy description of its critical points as cyclic polygons and a simple formula for the Morse index of a critical point. However, for planar polygons, the function $A$ in many cases is not a perfect Morse function. In particular, for an equilateral pentagonal linkage it has one extra local maximum (except for the global maximum) and one extra… 
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