Flow by the power of the Gauss curvature

Abstract

We prove that convex hypersurfaces in ${\mathbb{R}}^{n+1}$ contracting under the flow by any power $\alpha >\frac{1}{n+2}$ of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a smooth, uniformly convex self-similar contracting solution of the flow. Under additional central symmetry of the initial body we prove that the limit is the round sphere.

References in corpus (1)

• Deforming a hypersurface by Gauss curvature and support function

Cited by in corpus (5)

• Deforming a hypersurface by Gauss curvature and support function
• Uniqueness of closed self-similar solutions to the Gauss curvature flow
• The evolution of complete non-compact graphs by powers of Gauss curvature
• Nonparametric hypersurfaces moving by powers of Gauss curvature
• Stable solution of the log-Minkowski problem in the case of many hyperplane symmetries