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 contraction to the final
point. We prove existence and uniqueness of solutions for non-smooth initial
hypersurfaces, and develop upper and lower bounds on the speed and the curvature
independent of initial conditions. Applications are given to the flow by affine
normal and to the existence of non-spherical homothetically contracting
solutions.
