  We prove the local inequality $A \geq 8\pi|J|$, where $A$ and $J$ are the
area and angular momentum of any axially symmetric closed stable minimal
surface in an axially symmetric maximal initial data. From this theorem it is
proved that the inequality is satisfied for any surface on complete
asymptotically flat maximal axisymmetric data. In particular it holds for
marginal or event horizons of black holes.
