Resumen de Singular Yamabe-type problems with an asymptotically flat metric

Jiguang Bao, Yimei Li, Kun Wang

• In this paper, we study the asymptotic symmetry and local behavior of positive solutions at infinity to the equation −L g u=∣x∣ τ u n−2n+2+2τ outside a bounded set in Rn , where n≥3, −2<τ<0, and Lg 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 Rn ∖{0}.