The authors 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 self-similar contracting solution of the flow. Under additional central symmetry assumption on the initial body, they show that the limit is the round sphere for any \(\alpha\geq 1\).