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

Joseph Gordon, Gaiane Panina, Yana Teplitskaya

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (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
JournalBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Volume60
DOIs
Publication statusPublished - 6-Mar-2019
Externally publishedYes

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