Deforming a Convex Hypersurface by Anisotropic Curvature Flows

Abstract

In this paper, we consider a fully nonlinear curvature flow of a convex hypersurface in the Euclidean 𝑛-space. This flow involves 𝑘-th elementary symmetric function for principal curvature radii and a function of support function. Under some appropriate assumptions, we prove the long-time existence and convergence of this flow. As an application, we give the existence of smooth solutions to the Orlicz–Christoffel–Minkowski problem.

Keywords

• existence of solutions
• anisotropic curvature flow
• 35j96
• 35j75
• 53a15
• 53a07