Surfaces expanding by non-concave curvature functions (Q670316)

The authors investigate the flow of convex surfaces in three-dimensional simply-connected space forms of curvature \(\kappa=0,\pm 1\). The flow is expandig by \(F^{-\alpha}\), here \(F\) is a smooth, symmetric and homogeneous of degree one function of the principal curvatures of the surface. The power \(\alpha\) satisfies \(0<\alpha \le 1\) for \(\kappa=0,-1\) and \(\alpha=1\) for \(\kappa=1\). The long-time existence and convergence of the flow is shown. An important ingredient is an estimate for the pinching ratio along the flow.