1. CJM Online first
|The Weyl Problem With Nonnegative Gauss Curvature In Hyperbolic Space|
In this paper, we discuss the isometric embedding problem in hyperbolic space with nonnegative extrinsic curvature. We prove a priori bounds for the trace of the second fundamental form $H$ and extend the result to $n$-dimensions. We also obtain an estimate for the gradient of the smaller principal curvature in 2 dimensions.
Categories:53A99, 5J15, 58J05
2. 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