论文标题
批量保存的威尔莫尔流动
The volume-preserving Willmore flow
论文作者
论文摘要
我们考虑了$ \ Mathbb {r}^3 $中的一个封闭表面，该^$ the Villmore willmore流动，并证明了平滑解决方案的存在时间的下限。对于$8π$的球形初始表面，我们通过进行合适的爆炸并证明受约束的lojasiewicz-simon不等式来表现出长期存在和与圆形球体的融合。
We consider a closed surface in $\mathbb{R}^3$ evolving by the volume-preserving Willmore flow and prove a lower bound for the existence time of smooth solutions. For spherical initial surfaces with Willmore energy below $8π$ we show long time existence and convergence to a round sphere by performing a suitable blow-up and by proving a constrained Lojasiewicz-Simon inequality.
