A class of curvature flows expanded by support function and curvature function,Proceedings of the American Mathematical Society

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A class of curvature flows expanded by support function and curvature function
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-09-18 , DOI: 10.1090/proc/15189
Shanwei Ding , Guanghan Li

Abstract:In this paper, we consider a class of expanding flows of closed, smooth, uniformly convex hypersurfaces in Euclidean $\mathbb{R}^{n+1}$ with speed $u^\alpha f^\beta$ ( $\alpha , \beta \in \mathbb{R}^1$ ), where

is the support function of the hypersurface,

is a smooth, symmetric, homogenous of degree one, positive function of the principal curvature radii of the hypersurface. If $\alpha \leqslant 0<\beta \leqslant 1-\alpha$ , 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.

中文翻译：

一类由支撑函数和曲率函数扩展的曲率流

摘要：在本文中，我们考虑了一类以速度（）在欧几里得中的闭合，光滑，均匀凸超曲面的扩展流，其中超曲面的支撑函数是一阶对称，正函数的光滑，对称，齐次超曲面的主曲率半径如果，则证明流始终具有唯一的光滑且均匀凸的解，并且在归一化后平滑收敛到以原点为中心的圆形球体。 $\ mathbb {R} ^ {n + 1}$ $u ^ \ alpha f ^ \ beta$ $\ alpha，\ beta \ in \ mathbb {R} ^ 1$

$\ alpha \ leqslant 0 <\ beta \ leqslant 1- \ alpha$

更新日期：2020-10-19

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