Delaunay-type singular solutions for the fractional Yamabe problem

• Published in: Mathematische annalen Vol. 369; no. 1-2; pp. 597 - 626
• Main Authors: DelaTorre, Azahara, del Pino, Manuel, González, María del Mar, Wei, Juncheng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-10-2017; Springer Nature B.V
• Subjects: Mathematics; Mathematics and Statistics; Polar coordinates
• ISSN: 0025-5831; 1432-1807
• DOI: 10.1007/s00208-016-1483-1

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