Flow by powers of the Gauss curvature in space forms

In this paper, we prove that convex hypersurfaces under the flow by powers alpha > 0 of the Gauss curvature in space forms Nn+1 (K) of constant sectional curvature K (K = +/- 1) contract to a point in finite time T & lowast;. Moreover, convex hypersurfaces under the flow by power alpha > 1/n+2 curvature converge (after rescaling) to a limit which is the geodesic sphere in Nn+1 (K). This extends the known results in Euclidean space to space forms. (c) 2024 Elsevier Inc. All rights reserved.