论文标题
与Orlicz-Minkowski问题有关的广义高斯曲率流
A generalized Gauss curvature flow related to the Orlicz-Minkowski problem
论文作者
论文摘要
在本文中，研究了欧几里德$ n $ -space中凸出的高曲面的广义高斯曲率流。该流量与Orlicz-Minkowski问题密切相关，该问题涉及高斯曲率和支持功能的函数。在一些适当的假设下，我们证明了这种流动的长期存在和收敛性。作为副产品，获得了两个偶数溶液问题的存在结果，其中之一改善了已知结果。
In this paper a generalized Gauss curvature flow about a convex hypersurface in the Euclidean $n$-space is studied. This flow is closely related to the Orlicz-Minkowski problem, which involves Gauss curvature and a function of support function. Under some appropriate assumptions, we prove the long-time existence and convergence of this flow. As a byproduct, two existence results of solutions to the even Orlicz-Minkowski problem are obtained, one of which improves the known result.
