Trajectory Surfaces of Framed Curvature Flow
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914929421844480 |
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| author | Minarčík, Jiří Beneš, Michal |
| author_facet | Minarčík, Jiří Beneš, Michal |
| contents | This work introduces the framed curvature flow, a generalization of both the curve shortening flow and the vortex filament equation. Here, the magnitude of the velocity vector is still determined by the curvature, but its direction is given by an associated time-dependent moving frame. After establishing local existence and global estimates, we analyze the trajectory surfaces generated by different variations of this flow, specifically those leading to surfaces of constant mean or Gaussian curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Trajectory Surfaces of Framed Curvature Flow Minarčík, Jiří Beneš, Michal Differential Geometry Analysis of PDEs 53A10, 53E10, 53E40 (Primary) 53C42 (Secondary) This work introduces the framed curvature flow, a generalization of both the curve shortening flow and the vortex filament equation. Here, the magnitude of the velocity vector is still determined by the curvature, but its direction is given by an associated time-dependent moving frame. After establishing local existence and global estimates, we analyze the trajectory surfaces generated by different variations of this flow, specifically those leading to surfaces of constant mean or Gaussian curvature. |
| title | Trajectory Surfaces of Framed Curvature Flow |
| topic | Differential Geometry Analysis of PDEs 53A10, 53E10, 53E40 (Primary) 53C42 (Secondary) |
| url | https://arxiv.org/abs/2408.16855 |