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arXiv · 2210.06967

Unified results of compactness and existence for prescribing fractional $Q$-curvatures problem

Yan Li·Zhongwei Tang·Heming Wang·Ning Zhou
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Abstract

In this paper we study the problem of prescribing fractional $Q$-curvature of order $2\sigma$ for a conformal metric on the standard sphere $\Sn$ with $\sigma\in (0,n/2)$ and $n\geq2$. Compactness and existence results are obtained in terms of the flatness order $\beta$ of the prescribed curvature function $K$. Making use of integral representations and perturbation result, we develop a unified approach to obtain these results when $\beta\in [n-2\sigma,n)$ for all $\sigma\in (0,n/2)$. This work generalizes the corresponding results of Jin-Li-Xiong [Math. Ann. 369: 109--151, 2017] for $\beta\in (n-2\sigma,n)$.

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Yan Li, Zhongwei Tang, Heming Wang, Ning Zhou. 2022-10-13. Unified results of compactness and existence for prescribing fractional $Q$-curvatures problem. https://arxiv.org/abs/2210.06967

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