Uniqueness and minimality of Euler's elastica with monotone curvature
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914275810869248 |
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| author | Miura, Tatsuya Wheeler, Glen |
| author_facet | Miura, Tatsuya Wheeler, Glen |
| contents | For an old problem of Euler's elastica we prove the novel global property that every planar elastica with non-constant monotone curvature is uniquely minimal subject to the clamped boundary condition. We also partly extend this unique minimality to the length-penalised case; this result is new even in view of local minimality. As an application we prove uniqueness of global minimisers in the straightening problem for generic boundary angles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12771 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniqueness and minimality of Euler's elastica with monotone curvature Miura, Tatsuya Wheeler, Glen Analysis of PDEs Differential Geometry 49Q10 and 53A04 For an old problem of Euler's elastica we prove the novel global property that every planar elastica with non-constant monotone curvature is uniquely minimal subject to the clamped boundary condition. We also partly extend this unique minimality to the length-penalised case; this result is new even in view of local minimality. As an application we prove uniqueness of global minimisers in the straightening problem for generic boundary angles. |
| title | Uniqueness and minimality of Euler's elastica with monotone curvature |
| topic | Analysis of PDEs Differential Geometry 49Q10 and 53A04 |
| url | https://arxiv.org/abs/2402.12771 |