Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure

Abstract

In this article, we study the Musielak-Orlicz-Gauss image problem based on the Gauss curvature flow in Li et al. We deal with some cases in which there is no uniform estimate for the Gauss curvature flow. By the use of the topological method in Guang et al., a special initial condition is chosen such that the Gauss curvature flow converges to a solution of the Musielak-Orlicz-Gauss image problem.

Keywords

• gauss curvature flow
• monge-ampère equation
• musielak-orlicz-gauss image problem
• topological method
• 35j20
• 35k96
• 52a30