Qualitative Properties of Singular Solutions to the Fractional Yamabe Problem

Abstract

In this paper we are interested in the qualitative properties of the solutions to the fractional Yamabe problem in ${\mathbb{R}}^n$ which present an isolated singularity. In particular, we prove that the Morse index of any such solution is infinity. The proof uses a Emden Fowler type transformation, so that we can pass to a nonlocal 1D problem posed in $\mathbb{R}$.

arXiv comment16 pages; several typos and misprints have been corrected, current address for S. C-B. has been added