A compactness result for the CR Yamabe problem in three dimensions

2023/12/31 by Claudio Afeltra, Afeltra, Claudio
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2401.00906

openalex publication_date 2023/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the compactness of the set of solutions to the CR Yamabe problem on a compact strictly pseudoconvex CR manifold of dimension three whose blow-up manifolds at every point have positive p-mass. As a corollary we deduce that compactness holds for CR-embeddable manifolds which are not CR-equivalent to S³. The theorem is proved by blow-up analysis.

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