We prove that an extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class
of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data
represent non-stationary, axially symmetric black holes.
As a consequence, we obtain that any data in this class satisfy the inequality √J ≤ m, where m and J are the total mass and angular momentum of spacetime.