naa a22 4500 510811027 CHVBK 20180411083442.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s12220-011-9267-z doi (NATIONALLICENCE)springer-10.1007/s12220-011-9267-z Existence and Multiplicity Results for the Prescribed Webster Scalar Curvature Problem on Three CR Manifolds [Elektronische Daten] [Hichem Chtioui, Mohameden Ahmedou, Ridha Yacoub] 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 $\mathbb{S}^{3}$ 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. Mathematica Josephina, Inc., 2011 Webster scalar curvature nationallicence Critical point at infinity nationallicence Gradient flow nationallicence Intersection number nationallicence Morse index nationallicence Topological methods nationallicence Chtioui Hichem Département de Mathématiques, Faculté des Sciences de Sfax, Route de Soukra, Sfax, Tunisia aut Ahmedou Mohameden Mathematisches Institut der Universität Giessen, Arndtstrasse 2, 35392, Giessen, Germany aut Yacoub Ridha Institut Préparatoire aux Etudes d'Ingénieur de Monastir, Avenue Ibn Al Jazzar, 5019, Monastir, Tunisia aut Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 878-894 1050-6926 23:2<878 2013 23 12220 https://doi.org/10.1007/s12220-011-9267-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9267-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chtioui Hichem Département de Mathématiques, Faculté des Sciences de Sfax, Route de Soukra, Sfax, Tunisia aut NATIONALLICENCE 700 1- Ahmedou Mohameden Mathematisches Institut der Universität Giessen, Arndtstrasse 2, 35392, Giessen, Germany aut NATIONALLICENCE 700 1- Yacoub Ridha Institut Préparatoire aux Etudes d'Ingénieur de Monastir, Avenue Ibn Al Jazzar, 5019, Monastir, Tunisia aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 878-894 1050-6926 23:2<878 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer