Flow by powers of the Gauss curvature in space forms.

In this paper, we prove that convex hypersurfaces under the flow by powers α > 0 of the Gauss curvature in space forms N n + 1 (κ) of constant sectional curvature κ (κ = ± 1) contract to a point in finite time T ⁎. Moreover, convex hypersurfaces under the flow by power α > 1 n + 2 of the Gauss curvature converge (after rescaling) to a limit which is the geodesic sphere in N n + 1 (κ). This extends the known results in Euclidean space to space forms. [ABSTRACT FROM AUTHOR]