Evolution of convex hypersurfaces by powers of the mean curvature

We study the evolution of a closed, convex hypersurface in ℝⁿ⁺¹ in direction of its normal vector, where the speed equals a positive power k of the mean curvature. We show that the flow exists on a maximal, finite time interval, and that, approaching the final time, the surfaces contract to a point. The author was partially supported by a Schweizerische Nationalfonds grant No. 21-66743.01.