A Weighted L^2-Estimate of the Witten Spinor in Asymptotically   Schwarzschild Manifolds
  We derive a weighted $L^2$-estimate of the Witten spinor in a complete Riemannian spin manifold $(M^n,g)$ of non-negative scalar curvature which is asymptotically Schwarzschild. The interior geometry of $M$ enters this estimate only via the lowest eigenvalue of the square of the Dirac operator on a conformal compactification of $M$. 
Felix Finster, Margarita Kraus