Curvature at the infinity of asymptotically flat Einstein manifold

Abstract

In this paper, we construct coordinates at the infinity of an asymptotically flat end of a Ricci-flat manifold $(M_m,g)$ as long as the $L^{m/2}$ norm of the curvature is finite in this end. As applications, we can define a Weyl tensor at the infinity of $M$ and a version of renormalized volume following Biquard and Hein to ALE Ricci-flat manifolds/orbifolds of any dimension.

Fixed a computational error in Lemma 2.8; Fixed the proofs of Proposition 2.10, Theorem 3.5 and equation (6.9)