Extremal Area of Polygons sliding along Curves
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866914876653305856 |
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| author | Siersma, Dirk |
| author_facet | Siersma, Dirk |
| contents | In this paper we study the area function of polygons, where the vertices are sliding along curves. We give geometric criteria for the critical points and determine also the Hesse matrix at those points. This is the starting point for a Morse-theoretic approach, which includes the relation with the topology of the configuration spaces. Moreover the condition for extremal area gives rise to a new type of billiard: the inner area billiard. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_13978 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Extremal Area of Polygons sliding along Curves Siersma, Dirk Metric Geometry 58K05 In this paper we study the area function of polygons, where the vertices are sliding along curves. We give geometric criteria for the critical points and determine also the Hesse matrix at those points. This is the starting point for a Morse-theoretic approach, which includes the relation with the topology of the configuration spaces. Moreover the condition for extremal area gives rise to a new type of billiard: the inner area billiard. |
| title | Extremal Area of Polygons sliding along Curves |
| topic | Metric Geometry 58K05 |
| url | https://arxiv.org/abs/2211.13978 |