Optimal control in prescribing Webster scalar curvatures on 3-dimensional pseudo Hermitian manifolds

In this work, we give new existence and multiplicity results for the solutions of the prescription problem for the Webster scalar curvature on a 3-dimensional Pseudo Hermitian Manifold. The critical points of prescribed functions verify mixed conditions. We establish some Morse Inequalities at Infin...

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Bibliographic Details
Published inNonlinear analysis Vol. 127; pp. 235 - 262
Main Authors Gamara, Najoua, Amri, Amine, Guemri, Habiba
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.11.2015
Subjects
CR manifolds
Critical point at infinity
Curvature
Flatness condition
Inequalities
Infinity
Lower bounds
Manifolds
Mathematical analysis
Morse index
Scalars
Upper bounds
Webster scalar curvature
58E05
Flatness condition
53C21
53C15
Critical point at infinity
Morse index
57R70
CR manifolds
Webster scalar curvature
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Summary:In this work, we give new existence and multiplicity results for the solutions of the prescription problem for the Webster scalar curvature on a 3-dimensional Pseudo Hermitian Manifold. The critical points of prescribed functions verify mixed conditions. We establish some Morse Inequalities at Infinity and a Poincaré–Hopf type formula to give a lower bound on the number of solutions as well as an upper bound for the Morse index of such solutions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2015.05.035