A Weighted L^2-Estimate of the Witten Spinor in Asymptotically Schwarzschild Manifolds

Abstract

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 $M$.

arXiv comment21 pages, 1 figure, error in Lemma 5.1 corrected (published version)

References in corpus (1)

• Curvature Estimates in Asymptotically Flat Lorentzian Manifolds

Cited by in corpus (2)

• Some Curvature Problems in Semi-Riemannian Geometry
• Rigidity of conformal functionals on spheres