We prove some results on the existence and compactness of solutions of a fractional Nirenberg problem. The crucial ingredients of our proofs are the understanding of the blow up profiles and a Liouville theorem.
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Tianling Jin, YanYan Li, Jingang Xiong, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions. J. Eur. Math. Soc. 16 (2014), no. 6, pp. 1111–1171DOI 10.4171/JEMS/456