A Weighted $L^2$-Estimate of the Witten Spinor in Asymptotically Schwarzschild Manifolds
Printed: Oct 2007
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 $M$.
83C60 - Spinor and twistor methods; Newman-Penrose formalism
35Q75 - PDEs in connection with relativity and gravitational theory
35J45 - General theory of elliptic systems of PDE
58J05 - Elliptic equations on manifolds, general theory [See also 35-XX]