Unified results for existence and compactness in the prescribed fractional \(Q\)-curvature problem

DOI10.1007/S00030-024-00927-6arXiv2210.06967MaRDI QIDQ6127263

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Publication date: 12 April 2024

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Abstract: In this paper we study the problem of prescribing fractional $Q$-curvature of order $2sigma$ for a conformal metric on the standard sphere $Sn$ with $sigmain(0,n/2)$ and $ngeq2$. Compactness and existence results are obtained in terms of the flatness order $$ of the prescribed curvature function $K$. Making use of integral representations and perturbation result, we develop a unified approach to obtain these results when $$ for all $sigmain(0,n/2)$. This work generalizes the corresponding results of Jin-Li-Xiong [Math. Ann. 369: 109--151, 2017] for $$.

Full work available at URL: https://arxiv.org/abs/2210.06967

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