Flow by 𝜎_{𝑘} curvature to the Orlicz Christoffel-Minkowski problem

Abstract

In this paper, we consider the anisotropic curvature flow of smooth, origin-symmetric, uniformly convex hypersurfaces in R n + 1 \mathbb {R}^{n+1} . The flow exists for all time and converges smoothly to a solution of the even Orlicz Christoffel-Minkowski problem. Our proof also gives an approach to the solution of the L p L_p Christoffel-Minkowski problem.