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Search: MSC category 58J05 ( Elliptic equations on manifolds, general theory [See also 35-XX] )

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1. CJM 2014 (vol 67 pp. 107)

Chang, Jui-En; Xiao, Ling
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)

Finster, Felix; Kraus, Margarita
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

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