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

Published:2007-10-01
Printed: Oct 2007
• Felix Finster
• Margarita Kraus
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## 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 $M$.
 MSC Classifications: 83C60 - Spinor and twistor methods; Newman-Penrose formalism 35Q75 - PDEs in connection with relativity and gravitational theory 35J45 - General theory of elliptic systems of PDE58J05 - Elliptic equations on manifolds, general theory [See also 35-XX]

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