Existence results for the fractional Nirenberg problem
  We consider the fractional Nirenberg problem on the standard sphere $\mathbb{S}^n$ with $n\geq 4$. Using the theory of critical points at infinity, we establish an Euler-Hopf type formula and obtain some existence results for curvature satisfying assumptions of Bahri-Coron type. 
Yan-Hong Chen and Chungen Liu and Youquan Zheng
math.AP math.DG