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arXiv · 2508.16288

Curvature at the infinity of asymptotically flat Einstein manifold

Bing Wang·Hao Yin
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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.

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Bing Wang, Hao Yin. 2025-08-22. Curvature at the infinity of asymptotically flat Einstein manifold. https://doi.org/10.1090/btran%2F252

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