Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric

We prove that any positive solution of the Yamabe equation on an asymptotically flat n-dimensional manifold flatness order at least n−22 and n≤24 must converge infinity either to a fundamental Laplace operator Euclidean space or radial Fowler defined entire space. The is minimal required define ADM mass in general relativity; dimension 24 dividing validity compactness solutions problem. also such alternatives for bounded when n>24. these results by establishing appropriate asymptotic behavior near isolated singularity metric has n≤24, n>24 grows no faster than Laplacian singularity. These extend earlier L. Caffarelli, B. Gidas J. Spruck, N. Korevaar, R. Mazzeo, F. Pacard Schoen, conformally flat, work C.C. Chen C.S. Lin scalar curvature non-constant function with singular point, Marques not necessarily but smooth, three, four, five, as well recent similar second third authors six.