Willmore Flow of Complete Surfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914650110558208 |
|---|---|
| author | Li, Long-Sin |
| author_facet | Li, Long-Sin |
| contents | We consider the Willmore flow equation for complete, properly immersed surfaces in Rn. Given bounded geometry on the initial surface, we extend the result by Kuwert and Schätzle in 2002 and prove short time existence and uniqueness of the Willmore flow. We also show that a complete Willmore surface with low Willmore energy must be a plane, and that a Willmore flow with low initial energy and Euclidean volume growth must converge smoothly to a plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08692 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Willmore Flow of Complete Surfaces Li, Long-Sin Differential Geometry 53C40 53E10 53E40 53A05 We consider the Willmore flow equation for complete, properly immersed surfaces in Rn. Given bounded geometry on the initial surface, we extend the result by Kuwert and Schätzle in 2002 and prove short time existence and uniqueness of the Willmore flow. We also show that a complete Willmore surface with low Willmore energy must be a plane, and that a Willmore flow with low initial energy and Euclidean volume growth must converge smoothly to a plane. |
| title | Willmore Flow of Complete Surfaces |
| topic | Differential Geometry 53C40 53E10 53E40 53A05 |
| url | https://arxiv.org/abs/2212.08692 |