Area-perimeter duality in polygon spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866929426671861760 |
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| author | Khimshiashvili, Giorgi Panina, Gaiane Siersma, Dirk |
| author_facet | Khimshiashvili, Giorgi Panina, Gaiane Siersma, Dirk |
| contents | Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type of leaves are determined. The homology groups of the spaces of polygons with fixed area and perimeter are also determined. Besides, we extend the classical isoperimetric duality to all critical points. In conclusion a few general remarks on dual extremal problems in polygon spaces and beyond are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_03146 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Area-perimeter duality in polygon spaces Khimshiashvili, Giorgi Panina, Gaiane Siersma, Dirk Geometric Topology 52R70, 52B99 Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type of leaves are determined. The homology groups of the spaces of polygons with fixed area and perimeter are also determined. Besides, we extend the classical isoperimetric duality to all critical points. In conclusion a few general remarks on dual extremal problems in polygon spaces and beyond are given. |
| title | Area-perimeter duality in polygon spaces |
| topic | Geometric Topology 52R70, 52B99 |
| url | https://arxiv.org/abs/2002.03146 |