Curvature Estimates in Asymptotically Flat Lorentzian Manifolds

[摘要] We consider an asymptotically flat Lorentzian manifold ofdimension $(1,3)$. An inequality is derived which bounds theRiemannian curvature tensor in terms of the ADM energy in thegeneral case with second fundamental form. The inequalityquantifies in which sense the Lorentzian manifold becomes flat inthe limit when the ADM energy tends to zero.

[学科分类] 数学（综合）