Away from the central axis, we prove the stability of the positive mass theorem in the
sense
for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature
satisfying some additional technical assumptions. We also derive estimates for the
volumes of regions, the areas of axisymmetric surfaces, and the distances between
points within the manifolds.
Keywords
positive mass theorem, stability, small mass, axisymmetric