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

2022/10/13 by Yan Li, Li, Yan, Zhongwei Tang +4
Mathematics · #35B44 #35J35 #35R09 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2210.06967

openalex publication_date 2022/10/13 · openalex created_date 2022/10/15 · openalex updated_date 2026/07/28

Abstract

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

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