A generalized Gauss curvature flow related to the Orlicz-Minkowski problem

Abstract

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.

arXiv comment19 pages. arXiv admin note: text overlap with arXiv:2001.08862

References in corpus (7)

• The Logarithmic Minkowski Problem
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• General affine surface areas
• The Dual Orlicz-Brunn-Minkowski Theory
• On the uniqueness of $L_p$-Minkowski problems: the constant $p$-curvature case in ${\mathbb{R}}^3$
• Non-scale-invariant inverse curvature flows in Euclidean space
• The Orlicz version of the $L_p$ Minkowski problem on $S^{n-1}$ for $-n<p<0$

Cited by in corpus (1)

• Deforming a convex hypersurface by anisotropic curvature flows