Flowing the leaves of a foliation with normal speed given by the logarithm of general curvature functions (Q2066022)

An evolution of convex hypersurfaces in \(\mathbb{R}^{n+1}\) is considered with speeds \(-\log(F/f).\) Here \(F\) is a curvature function of the principal curvatures and \(f\) is a smooth positive function on the sphere \(S^n.\) It is shown that there is a distinct leaf such that the flow starting from this leaf converges to a translating solution of the flow equation. Inside this leaf the flow shrinks to a point, outside it expands to infinity.