  We examine the question of convergence of solutions to a geometric flow which
was introduced by Guan and Li for starshaped hypersurfaces in space forms and
generalized by Guan, Li, and Wang to the case of warped product spaces. We
obtain a convergence result under a condition on the optimal modulus of
continuity of the initial data. Moreover we show by examples that this
condition is optimal at least in the one-dimensional case.
