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We prove an inequality between horizon area and angular momentum for a classof axially symmetric black holes. This class includes initial conditions withan isometry which leaves fixed a two-surface. These initial conditions havebeen extensively used in the numerical evolution of rotating black holes. Theycan describe highly distorted black holes, not necessarily near equilibrium. Wealso prove the inequality on extreme throat initial data, extending previousresults.

Horizon area--angular momentum inequality for a class of axially symmetric black holes