论文标题
在$ \ mathbb {r}^3 $中扩展和翻译平均曲率流的孤子的频谱和索引上
On the spectrum and index of expanding and translating solitons of the mean curvature flow in $\mathbb{R}^3$
论文作者
论文摘要
在本文中，我们证明，具有有限$ l $ index的二维翻译孤子{r}^3 $对飞机或圆柱体是同型的，并且具有有限的$ l $ index and Exportightex Exportex and Sub Exported Exported Exported Everge Everment Everment Everment Eventment的二维自我expander具有有限的拓扑。我们还证明，翻译孤子和自我膨胀者具有有限的拓扑结构，前提是$ l $稳定运算符的底部从下面进行界限，并且其加权体积具有次指数的增长。
In this paper we prove that two-dimensional translating solitons in $\mathbb{R}^3$ with finite $L$-index are homeomorphic to a plane or a cylinder and that a two-dimensional self-expander with finite $L$-index and sub exponential weighted volume growth has finite topology. We also prove that translating solitons and self-expanders have finite topology, provided the bottom of the spectrum of the $L$-stability operator is bounded from below and their weighted volume have subexponential growth.
