Isoperimetric Inequality for Disconnected Regions
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866909370923614208 |
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| author | Sanki, Bidyut Vadnere, Arya |
| author_facet | Sanki, Bidyut Vadnere, Arya |
| contents | The discrete isoperimetric inequality in Euclidean geometry states that among all $n$-gons having a fixed perimeter $p$, the one with the largest area is the regular $n$-gon. The statement is true in spherical geometry and hyperbolic geometry as well.
In this paper, we generalize the discrete isoperimetric inequality to disconnected regions, i.e. we allow the area to be split between regions. We give necessary and sufficient conditions for the result (in Euclidean, spherical and hyperbolic geometry) to hold for multiple $n$-gons whose areas add up. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_07697 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Isoperimetric Inequality for Disconnected Regions Sanki, Bidyut Vadnere, Arya Geometric Topology The discrete isoperimetric inequality in Euclidean geometry states that among all $n$-gons having a fixed perimeter $p$, the one with the largest area is the regular $n$-gon. The statement is true in spherical geometry and hyperbolic geometry as well. In this paper, we generalize the discrete isoperimetric inequality to disconnected regions, i.e. we allow the area to be split between regions. We give necessary and sufficient conditions for the result (in Euclidean, spherical and hyperbolic geometry) to hold for multiple $n$-gons whose areas add up. |
| title | Isoperimetric Inequality for Disconnected Regions |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/1908.07697 |