Singular Yamabe-type problems with an asymptotically flat metric

In this paper, we study the asymptotic symmetry and local behavior of positive solutions at infinity to the equation -L₆u = |x|^u^n+2+2{n-2} outside a bounded set in R^n, where n 3, -2<<0, and L₆ is the conformal Laplacian with asymptotically flat Riemannian metric g. We prove that the solution, at, either converges to a fundamental solution of the Laplace operator on the Euclidean space, or is asymptotically close to a Fowler-type solution defined on R^n \0\.