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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.12609 |
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| _version_ | 1866917779849871360 |
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| author | Tabachnikov, Serge |
| author_facet | Tabachnikov, Serge |
| contents | An old theorem, due to Graustein, asserts that the average curvature of a plane oval is attained at least at four points. We present a proof by way of wave propagation and extend this result to the spherical and hyperbolic geometries - in the latter case, to horocyclically convex curves only. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12609 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A 4-point theorem: still another variation on an old theme Tabachnikov, Serge Differential Geometry An old theorem, due to Graustein, asserts that the average curvature of a plane oval is attained at least at four points. We present a proof by way of wave propagation and extend this result to the spherical and hyperbolic geometries - in the latter case, to horocyclically convex curves only. |
| title | A 4-point theorem: still another variation on an old theme |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2409.12609 |