Convergence of gradient flows on knotted curves
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918193923096576 |
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| author | Döhrer, Elias Freches, Nicolas |
| author_facet | Döhrer, Elias Freches, Nicolas |
| contents | We prove full convergence of gradient-flows of the arc-length restricted tangent point energies in the Hilbert-case towards critical points. This is done through a Łojasiewicz-Simon gradient inequality for these energies. In order to do so, we prove, that the tangent-point energies are anlytic on the manifold of immersed embeddings and that their Hessian is Fredholm with index zero on the manifold of arc-length parametrized curves. As a by-product, we also show that the metric on the manifold of embedded immersed curves, defined by the first author, is analytic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of gradient flows on knotted curves Döhrer, Elias Freches, Nicolas Classical Analysis and ODEs We prove full convergence of gradient-flows of the arc-length restricted tangent point energies in the Hilbert-case towards critical points. This is done through a Łojasiewicz-Simon gradient inequality for these energies. In order to do so, we prove, that the tangent-point energies are anlytic on the manifold of immersed embeddings and that their Hessian is Fredholm with index zero on the manifold of arc-length parametrized curves. As a by-product, we also show that the metric on the manifold of embedded immersed curves, defined by the first author, is analytic. |
| title | Convergence of gradient flows on knotted curves |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2511.07214 |