论文标题
一类通用的全线曲率流及其应用
A class of generalized fully nonlinear curvature flows and its applications
论文作者
论文摘要
在本文中，我们涉及涉及$ k $ th的总体非线性曲率流，其中$ k $的基本对称功能在Eulidean Space中的主曲率半径$ \ rnnn $，$ k $是整数，$ 1 \ leq K \ leq K \ leq k \ leq n-1 $。对于$ 1 \ leq k <n-1 $，基于一些初始数据，并约束在单位球体上定义的平滑正函数$ \ sn $，我们获得了该流量的长时间存在和收敛性。特别是，应以$ k = n-1 $得出相同的结果，而不会对光滑的正函数进行任何限制。
In this paper, we concern a generalized fully nonlinear curvature flow involving $k$-th elementary symmetric function for principal curvature radii in Eulidean space $\rnnn$, $k$ is an integer and $1\leq k\leq n-1$. For $1\leq k< n-1$, based on some initial data and constrains on smooth positive function defined on the unit sphere $\sn$, we obtain the long time existence and convergence of the flow. Especially, the same result shall be derived for $k=n-1$ without any constraint on the smooth positive function.
