Polygons with prescribed edge slopes: configuration space and extremal points of perimeter

Joseph Gordon, Gaiane Panina, Yana Teplitskaya

Research output

1 Citation (Scopus)

Abstract

We describe the configuration space S of polygons with prescribed edge slopes, and study the perimeter P as a Morse function on S. We characterize critical points of P (these are tangential polygons) and compute their Morse indices. This setup is motivated by a number of results about critical points and Morse indices of the oriented area function defined on the configuration space of polygons with prescribed edge lengths (flexible polygons). As a by-product, we present an independent computation of the Morse index of the area function (obtained earlier by Panina and Zhukova).

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalBeitrage zur Algebra und Geometrie
Volume60
Issue number1
DOIs
Publication statusPublished - 12 Mar 2019

Scopus subject areas

  • Geometry and Topology
  • Algebra and Number Theory

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