An application of dual convex bodies to the inverse Gauss curvature flow

Abstract

By means of dual convex bodies, we obtain regularity of solutions to the expanding Gauss curvature flows with homogeneity degrees $-p$, $0<p<1$. At the end, we remark that our method can also be used to obtain regularity of solutions to the shrinking Gauss curvature flows with homogeneity degrees less than one.

To appear in Proc. Amer. Math. Soc

References in corpus (4)

• Non-scale-invariant inverse curvature flows in Euclidean space
• Entropy and a convergence theorem for Gauss curvature flow in high dimension
• Surfaces moving by powers of Gauss curvature
• Contracting convex hypersurfaces by curvature