论文标题
在IIB型溶液的精确渐近学上，平均曲率流量
On the precise asymptotics of Type-IIb solutions to mean curvature flow
论文作者
论文摘要
在本文中，我们研究了平均曲率流的非2型IIB溶液的精确渐近造型。确切地说，对于每个实际数字$γ> 0 $，我们在旋转对称的类别中构建平均曲率流解决方案，以下精确的渐近差为$ t \近乎近\ \：（1）高度表面（一个umbilical Point）的最高曲率浓度（一个Umbilical Point）（一个umbilical Point），并以type-ib rave $ 1 $（2tt）$（2tt）$（2tt）$（2tt）$（2tt）。 （2）在尖端的邻域中，溶液的类型IIB炸毁会收敛于被称为“碗孔”的翻译。 （3）在空间无穷大范围内，高表面具有确切的增长率，具体取决于$γ$。
In this paper, we study the precise asymptotics of noncompact Type-IIb solutions to the mean curvature flow. Precisely, for each real number $γ>0$, we construct mean curvature flow solutions, in the rotationally symmetric class, with the following precise asymptotics as $t\nearrow\infty$: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilical point) and blows up at the Type-IIb rate $(2t+1)^{(γ-1)/2}$. (2) In a neighbourhood of the tip, the Type-IIb blow-up of the solution converges to a translating soliton known as the bowl soliton. (3) Near spatial infinity, the hypersurface has a precise growth rate depending on $γ$.
