The length-preserving elastic flow with free boundary on hypersurfaces in $\mathbb{R}^n$
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| Format: | Preprint |
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2025
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| _version_ | 1866917959136444416 |
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| author | Dall'Acqua, Anna Schlierf, Manuel |
| author_facet | Dall'Acqua, Anna Schlierf, Manuel |
| contents | We study the length-preserving elastic flow of curves in arbitrary codimension with free boundary on hypersurfaces. This constrained gradient flow is given by a nonlocal evolution equation with nonlinear higher-order boundary conditions. We prove global existence and subconvergence to critical points. The proof strategy involves a careful treatment of short-time existence, uniqueness, and parabolic energy estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13219 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The length-preserving elastic flow with free boundary on hypersurfaces in $\mathbb{R}^n$ Dall'Acqua, Anna Schlierf, Manuel Analysis of PDEs Differential Geometry Primary 53E40, Secondary 35G31, 35B40 We study the length-preserving elastic flow of curves in arbitrary codimension with free boundary on hypersurfaces. This constrained gradient flow is given by a nonlocal evolution equation with nonlinear higher-order boundary conditions. We prove global existence and subconvergence to critical points. The proof strategy involves a careful treatment of short-time existence, uniqueness, and parabolic energy estimates. |
| title | The length-preserving elastic flow with free boundary on hypersurfaces in $\mathbb{R}^n$ |
| topic | Analysis of PDEs Differential Geometry Primary 53E40, Secondary 35G31, 35B40 |
| url | https://arxiv.org/abs/2503.13219 |