Existence of optimal flat ribbons
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911899390574592 |
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| author | Blatt, Simon Raffaelli, Matteo |
| author_facet | Blatt, Simon Raffaelli, Matteo |
| contents | We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in $\mathbb{R}^{3}$ can be extended to an infinitely narrow flat ribbon having minimal bending energy. We also show that, in general, minimizers are not free of planar points, yet such points must be isolated under the mild condition that the torsion does not vanish. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07311 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Existence of optimal flat ribbons Blatt, Simon Raffaelli, Matteo Differential Geometry Classical Analysis and ODEs 49Q10, 53A05 (Primary) 49J45, 74B20, 74K20 (Secondary) We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in $\mathbb{R}^{3}$ can be extended to an infinitely narrow flat ribbon having minimal bending energy. We also show that, in general, minimizers are not free of planar points, yet such points must be isolated under the mild condition that the torsion does not vanish. |
| title | Existence of optimal flat ribbons |
| topic | Differential Geometry Classical Analysis and ODEs 49Q10, 53A05 (Primary) 49J45, 74B20, 74K20 (Secondary) |
| url | https://arxiv.org/abs/2307.07311 |