Existence and Multiplicity results for the prescribed Webster Scalar Curvature Problem on three C R manifolds

2009/06/02 by Hichem Chtioui, Chtioui, H., Mohameden Ould Ahmedou +3
Mathematics · #35J65 #53C15 #53C21 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0906.0475

openalex publication_date 2009/06/02 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the existence of contact forms of prescribed Webster scalar curvature on a 3-dimensional CR compact manifold locally conformally CR equivalent to the unit sphere \mathbbS³ of ℂ². Due to Kazdan-Warner type obstructions, conditions on the function H to be realized as a Webster scalar curvature have to be given. We prove new existence results based on a new type of Euler-Hopf type formula. Our argument gives an upper bound on the Morse index of the obtained solution. We also give a lower bound on the number of conformal contact forms having the same Webster scalar curvature.

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