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

Published online by Cambridge University Press:  20 November 2018

Felix Finster  and
Margarita Kraus
Felix Finster
Affiliation:
NWF I–Mathematik, Universität Regensburg, 93040 Regensburg, Germany email: Felix.Finster@mathematik.uni-regensburg.de, Margarita.Kraus@mathematik.uni-regensburg.de
Margarita Kraus
Affiliation:
NWF I–Mathematik, Universität Regensburg, 93040 Regensburg, Germany email: Felix.Finster@mathematik.uni-regensburg.de, Margarita.Kraus@mathematik.uni-regensburg.de
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Abstract

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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 $M$.

Keywords

83C6035Q7535J4558J05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 5 , 01 October 2007 , pp. 943 - 965
Copyright
Copyright © Canadian Mathematical Society 2007

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