论文标题
曲率非均匀功能的凸出曲面收缩
Contraction of convex hypersurfaces by nonhomogeneous functions of curvature
论文作者
论文摘要
最近的一篇文章LI和LV考虑了曲率的某些非均匀函数的凸超曲面的收缩，在某些情况下，在有限时间内的点收敛到有限的点，在某些情况下，速度是一度均等，凹面，凹面和逆凹的函数的原理曲率的函数。在本文中，我们将结果扩展到类似于其他早期工作类似的其他各种情况，我们表明，在所有情况下，在最初的高表情上都假定了足够的捏合条件，那么在适当的重新缩放下，最终点是渐近的圆形，并且收敛性在$ c^\ infty $ topopology中是指数的。
A recent article Li and Lv considered contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in certain cases where the speed is a function of a degree-one homogeneous, concave and inverse concave function of the principle curvatures. In this article we extend the result to various other cases that are analogous to those considered in other earlier work, and we show that in all cases, where sufficient pinching conditions are assumed on the initial hypersurface, then under suitable rescaling the final point is asymptotically round and convergence is exponential in the $C^\infty$-topology.
