论文标题
高斯曲率流到双重orlicz-minkowski问题
Flow by Gauss curvature to Dual Orlicz-Minkowski problems
论文作者
论文摘要
在本文中，我们研究了严格凸的归一化各向异性高斯曲率流，欧几里得空间中的封闭性超曲面r^n+1。我们证明该流量一直存在，并顺利收敛到Monge-Amp`型方程的独特，严格的凸解决方案。我们的论点在平滑类别中提供了一个抛物线证明，以实现Zhu，Xing和Ye引入的双重Orlicz-Minkowski问题的解决方案。
In this paper we study a normalised anisotropic Gauss curvature flow of strictly convex, closed hypersurfaces in the Euclidean space R^n+1. We prove that the flow exists for all time and converges smoothly to the unique, strictly convex solution of a Monge-Amp`ere type equation. Our argument provides a parabolic proof in the smooth category for the existence of solutions to the Dual Orlicz-Minkowski problem introduced by Zhu, Xing and Ye.
