Comment on "Horizon area- Angular momentum inequality for a class of axially symmetric black holes" [arXiv:1012.2413]

We extend the results presented by Ace~na $\mathit{\text{et}}\mathit{\text{al}}$ in the afore mentioned paper, [arXiv:1012.2413], to the case of axisymmetric, maximal initial data which are invariant under an inversion transformation.