  For axisymmetric evolution of isolated systems, we prove that there exists a
gauge such that the total mass can be written as a positive definite integral
on the spacelike hypersurfaces of the foliation and the integral is constant
along the evolution. The conserved mass integral controls the square of the
extrinsic curvature and the square of first derivatives of the intrinsic
metric. We also discuss applications of this result for the global existence
problem in axial symmetry.
