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A Weighted ${{L}^{2}}$-Estimate of the Witten Spinor in Asymptotically Schwarzschild Manifolds
Felix Finster, Margarita Kraus
Journal:

Canadian Journal of Mathematics / Volume 59 / Issue 5 / 01 October 2007

Published online by Cambridge University Press:

20 November 2018, pp. 943-965

Print publication:

01 October 2007
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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 $M$.