Extremal areas of polygons with fixed perimeter
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866916329776218112 |
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| author | Khimshiashvili, Giorgi Panina, Gaiane Siersma, Dirk |
| author_facet | Khimshiashvili, Giorgi Panina, Gaiane Siersma, Dirk |
| contents | We consider the configuration space of planar $n$-gons with fixed perimeter, which is diffeomorphic to the complex projective space $\mathbb{C}P^{n-2}$. The oriented area function has the minimal number of critical points on the configuration space. We describe its critical points (these are regular stars) and compute their indices when they are Morse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_07521 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Extremal areas of polygons with fixed perimeter Khimshiashvili, Giorgi Panina, Gaiane Siersma, Dirk Geometric Topology We consider the configuration space of planar $n$-gons with fixed perimeter, which is diffeomorphic to the complex projective space $\mathbb{C}P^{n-2}$. The oriented area function has the minimal number of critical points on the configuration space. We describe its critical points (these are regular stars) and compute their indices when they are Morse. |
| title | Extremal areas of polygons with fixed perimeter |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/1805.07521 |