Motion of hypersurfaces by Gauss curvature
Motion of hypersurfaces by Gauss curvature
We consider n-dimensional convex Euclidean hypersurfaces moving with normal velocity proportional to a positive power α of the Gauss curvature.We prove that hypersurfaces contract to points in finite time, and for α ∈ (1/(n + 2], 1/n] we also prove that in the limit the solutions evolve purely by homothetic …