论文标题
通过支撑功能和曲率功能扩展的一类曲率流量
A class of curvature flows expanded by support function and curvature function
论文作者
论文摘要
In this paper, we consider an expanding flow of closed, smooth, uniformly convex hypersurface in Euclidean \mathbb{R}^{n+1} with speed u^αf^β(α, β\in\mathbb{R}^1), where u is support function of the hypersurface, f is a smooth, symmetric, homogenous of degree one, positive function of the principal曲率半径。如果α\ leq 0 <β\ leq 1-α，我们证明该流程一直具有独特的平滑且均匀的凸溶液，并在归一化后平稳地收敛到以原点为中心的圆形球体。
In this paper, we consider an expanding flow of closed, smooth, uniformly convex hypersurface in Euclidean \mathbb{R}^{n+1} with speed u^αf^β(α, β\in\mathbb{R}^1), where u is support function of the hypersurface, f is a smooth, symmetric, homogenous of degree one, positive function of the principal curvature radii of the hypersurface. If α\leq 0<β\leq 1-α, we prove that the flow has a unique smooth and uniformly convex solution for all time, and converges smoothly after normalization, to a round sphere centered at the origin.
