Embeddedness and graphicality of the elastic flow for complete curves
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911122772197376 |
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| author | Miura, Tatsuya Rupp, Fabian |
| author_facet | Miura, Tatsuya Rupp, Fabian |
| contents | We study positivity-preserving properties for the elastic flow of non-compact, complete curves in Euclidean space. Despite the fact that the canonical elastic energy is infinite in this context, we extend our recent work based on the adapted elastic energy to derive nontrivial optimal thresholds for maintaining planar embeddedness and graphicality, respectively. We also obtain a new Li--Yau type inequality for complete planar curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embeddedness and graphicality of the elastic flow for complete curves Miura, Tatsuya Rupp, Fabian Analysis of PDEs Differential Geometry 53E40 (primary), 53A04, 49Q10 (secondary) We study positivity-preserving properties for the elastic flow of non-compact, complete curves in Euclidean space. Despite the fact that the canonical elastic energy is infinite in this context, we extend our recent work based on the adapted elastic energy to derive nontrivial optimal thresholds for maintaining planar embeddedness and graphicality, respectively. We also obtain a new Li--Yau type inequality for complete planar curves. |
| title | Embeddedness and graphicality of the elastic flow for complete curves |
| topic | Analysis of PDEs Differential Geometry 53E40 (primary), 53A04, 49Q10 (secondary) |
| url | https://arxiv.org/abs/2508.18979 |