Andrews, BenGuan, PengfeiNi, Lei2016-12-192016-12-190001-8708http://hdl.handle.net/1885/111424We prove that convex hypersurfaces in Rⁿ⁺¹ contracting under the flow by any power α > 1/n+2 source 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 for α≥1.application/pdf© 2016 ElsevierEntropyGauss CurvatureMonotonicityRegularity EstimatesCurvature ImageEntropy Stability Estimates201610.1016/j.aim.2016.05.008