数学
正多边形
曲率
流量平均曲率
算法
几何学
平均曲率
作者
Qiang Guang,Qi-Rui Li,Xu‐Jia Wang
摘要
In this paper, we study the existence of solutions to the centroaffine Minkowski problem, namely the existence of closed convex hypersurfaces in the Euclidean space R n + 1 \mathbb {R}^{n+1} with prescribed centroaffine curvature. This problem can be described as a variational problem with a functional resembling Kantorovich’s dual functional in optimal transportation. By using the Gauss curvature flow, we obtain new conditions for the existence of solutions to the problem.
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