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.

arXiv comment19 pages. arXiv admin note: text overlap with arXiv:2005.02376

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