  We consider flows with normal velocities equal to powers strictly larger than
one of the Gauss curvature. Under such flows closed strictly convex surfaces
converge to points. In his work on the square of the norm of the second
fundamental form, Schn\"urer proposes criteria for selecting quantities that
are suitable for proving convergence to a round point. Such monotone quantities
exist for many normal velocities, including the Gauss curvature, some powers
larger than one of the mean curvature, and some powers larger than one of the
norm of the second fundamental form. In this paper, we show that no such
quantity exists for any powers larger than one of the Gauss curvature.
