The Willmore flow with prescribed isoperimetric ratio
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866914679274602496 |
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| author | Rupp, Fabian |
| author_facet | Rupp, Fabian |
| contents | We introduce a non-local $L^2$-gradient flow for the Willmore energy of immersed surfaces which preserves the isoperimetric ratio. For spherical initial data with energy below an explicit threshold, we show long-time existence and convergence to a Helfrich immersion. This is in sharp contrast to the locally constrained flow, where finite time singularities occur. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_02579 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Willmore flow with prescribed isoperimetric ratio Rupp, Fabian Analysis of PDEs Differential Geometry 53E40 (primary), 35B40, 35K41 (secondary) We introduce a non-local $L^2$-gradient flow for the Willmore energy of immersed surfaces which preserves the isoperimetric ratio. For spherical initial data with energy below an explicit threshold, we show long-time existence and convergence to a Helfrich immersion. This is in sharp contrast to the locally constrained flow, where finite time singularities occur. |
| title | The Willmore flow with prescribed isoperimetric ratio |
| topic | Analysis of PDEs Differential Geometry 53E40 (primary), 35B40, 35K41 (secondary) |
| url | https://arxiv.org/abs/2106.02579 |