The Willmore flow of tori of revolution
- We study long-time existence and asymptotic behavior for the L2-gradient flow of the Willmore energy, under the condition that the initial datum is a torus of revolution. We show that if an initial datum has Willmore energy below 8π then the solution of the Willmore flow converges for t→∞ to the Clifford torus, possibly rescaled and translated. The energy threshold of 8π turns out to be optimal for such a convergence result. We give an application to the conformally constrained Willmore minimization problem.
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| Author: | Anna Dall'Acqua, Marius Müller, Reiner Schätzle, Adrian Spener |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1170975 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/117097 |
| ISSN: | 1948-206XOPAC |
| ISSN: | 2157-5045OPAC |
| Parent Title (English): | Analysis & PDE |
| Publisher: | Mathematical Sciences Publishers |
| Place of publication: | Berkeley, CA |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2024/11/27 |
| Volume: | 17 |
| Issue: | 9 |
| First Page: | 3079 |
| Last Page: | 3124 |
| DOI: | https://doi.org/10.2140/apde.2024.17.3079 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
