Randomized trial constructs coordinates for curvature at infinity in asymptotically flat Ricci-flat manifolds, suggesting new applications.
In this paper, we construct coordinates at the infinity of an asymptotically flat end of a Ricci-flat manifold ( M m , g ) (Mᵐ,g) as long as the L m / 2 Lm/2 norm of the curvature is finite in this end. As applications, we can define a Weyl tensor at the infinity of M M and a version of renormalized volume following Biquard and Hein to ALE Ricci-flat manifolds/orbifolds of any dimension.
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Wang et al. (2026) studied this question.