The Nirenberg problem and its generalizations: a unified approach
The authors aim to develop a unified approach to establish blow-up profiles, compactness and existence of positive solutions of the conformally invariant equations \(P_{\sigma }(v)=K\upsilon ^{\frac{n+2\sigma }{n-2\sigma }}\) on the standard unit sphere \(\mathbb{S}^{n}\) for all \(\sigma \in (0,n/2)\), using integral representations. When \(\sigma =1\), it is the prescribing scalar curvature problem or the Nirenberg problem, and when \(\sigma =2\), it is the prescribing \(Q\)-curvature problem.
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