1. CJM 2007 (vol 59 pp. 943)
|A Weighted $L^2$-Estimate of the Witten Spinor in Asymptotically Schwarzschild Manifolds |
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 $M$.
Categories:83C60, 35Q75, 35J45, 58J05
2. CJM 2005 (vol 57 pp. 708)
|Curvature Estimates in Asymptotically Flat Lorentzian Manifolds |
We consider an asymptotically flat Lorentzian manifold of dimension $(1,3)$. An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality quantifies in which sense the Lorentzian manifold becomes flat in the limit when the ADM energy tends to zero.
Categories:53C21, 53C27, 83C57