  We analyze the level sets of the norm of the Witten spinor in an
asymptotically flat Riemannian spin manifold of positive scalar curvature.
Level sets of small area are constructed. We prove curvature estimates which
quantify that, if the total mass becomes small, the manifold becomes flat with
the exception of a set of small surface area. These estimates involve either a
volume bound or a spectral bound for the Dirac operator on a conformal
compactification, but they are independent of the isoperimetric constant.
