A recent article Li and Lv (J. Geom. Anal. 30: 417–447, 2020) 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.

Li和Lv（J. Geom。Anal。30：417–447，2020）的最新文章认为凸超曲面通过某些非齐次的曲率函数收缩，在某些情况下在有限的时间内收敛到点，而速度是函数的函数。主曲率的一阶齐次，凹和反凹函数。在本文中，我们将结果扩展到与其他早期工作中所考虑的情况类似的其他各种情况，并且我们表明，在所有情况下，假设初始超曲面上有足够的挤压条件，然后在适当缩放后，最终点为在（（C ^ \ infty \）-拓扑中，渐近圆形和收敛性是指数级的。