Quermassintegral preserving curvature flow in Hyperbolic space
Quermassintegral preserving curvature flow in Hyperbolic space
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DOI：
10.1007/s00039-018-0456-9
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发表时间：
2018-07
影响因子：
2.2
通讯作者：
B. Andrews;Yong Wei
中科院分区：
文献类型：
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作者：
B. Andrews;Yong Wei
本文考虑双曲空间中闭凸超曲面的quermass保积分流，其速度由主曲率的一次齐次对称、严格增的光滑函数f的任意正幂给出，该函数f是反凹的，其对偶f * 在正锥的边界上趋于零.证明了如果初始超曲面是凸的，则流的解成为严格h-凸的，且流在光滑拓扑中指数收敛于测地球.
We consider the quermassintegral preserving flow of closedh-convexhypersurfaces in hyperbolic space with the speed given by any positive power of a smooth symmetric, strictly increasing, and homogeneous of degree one functionfof the principal curvatures which is inverse concave and has dualf*approaching zero on the boundary of the positive cone. We prove that if the initial hypersurface ish-convex, then the solution of the flow becomes strictlyh-convexfort> 0, the flow exists for all time and converges to a geodesic sphere exponentially in the smooth topology.