A gluing approach for the fractional Yamabe problem with isolated   singularities
  We construct solutions for the fractional Yamabe problem that are singular at a prescribed number of isolated points. This seems to be the first time that a gluing method is successfully applied to a non-local problem. The main step is an infinite-dimensional Lyapunov-Schmidt reduction method, that reduces the problem to an (infinite dimensional) Toda type system. 
Weiwei Ao, Azahara DelaTorre, Maria del Mar Gonzalez, Juncheng Wei
math.AP