Polygons with prescribed edge slopes: configuration space and extremal points of perimeter
| Autor: | Yana Teplitskaya, Joseph Gordon, Gaiane Panina |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Algebra and Number Theory
Computation 010102 general mathematics 0211 other engineering and technologies 02 engineering and technology Function (mathematics) Algebraic geometry Computer Science::Computational Geometry Edge (geometry) 01 natural sciences Critical point (mathematics) Perimeter Combinatorics Geometry and Topology Configuration space 0101 mathematics 021101 geological & geomatics engineering Mathematics Morse theory |
| Zdroj: | Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 60:1-15 |
| ISSN: | 2191-0383 0138-4821 |
| DOI: | 10.1007/s13366-018-0409-3 |
| Popis: | We describe the configuration space $$\mathbf {S}$$ of polygons with prescribed edge slopes, and study the perimeter $${\mathcal {P}}$$ as a Morse function on $$\mathbf {S}$$ . We characterize critical points of $${\mathcal {P}}$$ (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). |
| Databáze: | OpenAIRE |
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