摘要
在这份报纸，我们减一个外部力量领域由吝啬的弯曲的力量学习 hypersurfaces 的进化。我们证明当力量是 2 时，流动在一些条件下面在所有时间有一个长期的光滑的答案。那些条件是起始的 submanifolds 上的第二张基本表格不太大，与它的任何顺序衍生物，外部力量领域被围住，并且这个领域与它的特征值是凸的令人满意捏不平等。
In this paper, we study the evolution of hypersurfaces by powers of mean curvature minus an external force field. We prove that when the power is 2, the flow has a long-time smooth solution for all time under some conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is convex with its eigenvalues satisfying a pinch inequality.
基金
This work was supported in part by the National Natural Science Foundation of China （Grant No. 11026121）.
