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Optimal control in prescribing Webster scalar curvatures on 3-dimensional pseudo Hermitian manifolds
Journal article   Peer reviewed

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

Najoua Gamara, Amine Amri and Habiba Guemri
Nonlinear analysis, Vol.127, pp.235-262
11/2015
DOI: https://doi.org/10.1016/j.na.2015.05.035

Abstract

CR manifolds Critical point at infinity Flatness condition Morse index Webster scalar curvature
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.

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