A perturbation result for the Webster scalar curvature problem on the CR sphere

We consider the problem of prescribing the Webster scalar curvature on the unit sphere of Cn+1. Using a perturbation method, we obtain existence results for curvatures close to a positive constant and satisfying an assumption of Bahri–Coron type. On considère le problème de déterminer la courbure sc...

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Bibliographic Details
Published in:Journal de mathématiques pures et appliquées 2002-10, Vol.81 (10), p.983-997
Main Authors: Malchiodi, Andrea, Uguzzoni, Francesco
Format: Article
Language:English
Subjects:
Differential geometry
Exact sciences and technology
Geometry
Mathematics
Perturbation methods
Sciences and techniques of general use
Subelliptic equations
Webster curvature
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Summary:We consider the problem of prescribing the Webster scalar curvature on the unit sphere of Cn+1. Using a perturbation method, we obtain existence results for curvatures close to a positive constant and satisfying an assumption of Bahri–Coron type. On considère le problème de déterminer la courbure scalaire de Webster sur la sphère unitaire de Cn+1. En utilisant une méthode perturbative nous avons démontré l'existence pour des courbures proches d'une constante positive lorsque elle satisfont en plus une hypothèse du type Bahri–Coron.
ISSN:0021-7824
DOI:10.1016/S0021-7824(01)01249-1