论文标题
革命的摩尔摩托
The Willmore Flow of Tori of Revolution
论文作者
论文摘要
在初始基准是革命的条件下，我们研究了Willmore Energy的$ l^2 $差异流的长期存在和渐近行为。我们表明，如果初始基准的Willmore Energy低于$8π$，那么Willmore Flow的解决方案收敛于$ t \ rightarrow \ infty $ to Clifford torus to clifford torus，可能会重新定制和翻译。 $8π$的能源阈值对于这种收敛结果是最佳的。我们将适用于同型限制的Willmore最小化问题的应用。
We study long-time existence and asymptotic behavior for the $L^2$-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 $t \rightarrow \infty$ 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.
