Delaunay-type singular solutions for the fractional Yamabe Problem

Abstract

We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity $(-Δ)^γw = c_{n, γ} w^{\frac{n+2γ}{n-2γ}}, w>0 \ \mbox{in} \ \mathbb{R}^n \backslash \{0\}$ We follow a variational approach, in which the key is the computation of the fractional Laplacian in polar coordinates.

21 pages