|
|||||
 |
|
|
|
|
|
|
The Willmore flow of
tori of revolution
Anna Dall’Acqua, Marius Müller, Reiner Schätzle and Adrian Spener |
|
Vol. 17 (2024), No. 9, 3079–3124
|
 |
Abstract |
|
We study long-time existence and asymptotic behavior for the -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 then the solution of the Willmore flow converges for to the Clifford torus, possibly rescaled and translated. The energy threshold of turns out to be optimal for such a convergence result. We give an application to the conformally constrained Willmore minimization problem. |
Keywords
Willmore flow, torus of revolution, Clifford torus,
conformal class
|
Mathematical Subject Classification
Primary: 53E40
Secondary: 49Q20, 58E30
|
Milestones
Received: 22 March 2022
Revised: 19 June 2023
Accepted: 1 August 2023
Published: 1 November 2024
|
Authors |
| Anna Dall’Acqua | |
| Institute für Angewandte
Analysis Universität Ulm Ulm Germany |
|
| Marius Müller | |
| Institut für Mathematik Universität Augsburg Augsburg Germany |
|
| Reiner Schätzle | |
| Fachbereich Mathematik Eberhard-Karls-Universität Tübingen Tübingen Germany |
|
| Adrian Spener | |
| Institut für Angewandte
Analysis Universität Ulm Ulm Germany |
|
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
Open Access made possible by participating institutions via Subscribe to Open.
