There exists a scenario of a proof of the general Penrose inequality that requires a convexity property and the no-twist condition of a foliation of the Cauchy hypersurface. This paper shows that the no-twist condition can be removed and that, in the Schwarzschild geometry with linear axial perturbations, there do exist foliations that are convex in the required sense.

PACS numbers: 04.20.--q, 04.20.Dw