Dans cette Note nous considérons le problème dʼexistence de métriques conformes avec courbure scalaire prescrite, sur la sphère standard , . Nous donnons de nouveaux résultats dʼexistence et de multiplicité reposant sur un nouveau type de formule dʼEuler–Hopf. Nos arguments ont également lʼavantage dʼétendre des résultats bien connus de Y. Li (1995) [10].
In this Note, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere , . We give new existence and multiplicity results based on a new Euler–Hopf formula type. Our argument also has the advantage of extending the well known results due to Y. Li (1995) [10].
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@article{CRMATH_2012__350_11-12_583_0, author = {Ben Mahmoud, Randa and Chtioui, Hichem and Rigane, Afef}, title = {On the prescribed scalar curvature problem on $ {S}^{n}$: {The} degree zero case}, journal = {Comptes Rendus. Math\'ematique}, pages = {583--586}, publisher = {Elsevier}, volume = {350}, number = {11-12}, year = {2012}, doi = {10.1016/j.crma.2012.06.012}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.06.012/} }
TY - JOUR AU - Ben Mahmoud, Randa AU - Chtioui, Hichem AU - Rigane, Afef TI - On the prescribed scalar curvature problem on $ {S}^{n}$: The degree zero case JO - Comptes Rendus. Mathématique PY - 2012 SP - 583 EP - 586 VL - 350 IS - 11-12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.06.012/ DO - 10.1016/j.crma.2012.06.012 LA - en ID - CRMATH_2012__350_11-12_583_0 ER -
%0 Journal Article %A Ben Mahmoud, Randa %A Chtioui, Hichem %A Rigane, Afef %T On the prescribed scalar curvature problem on $ {S}^{n}$: The degree zero case %J Comptes Rendus. Mathématique %D 2012 %P 583-586 %V 350 %N 11-12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.06.012/ %R 10.1016/j.crma.2012.06.012 %G en %F CRMATH_2012__350_11-12_583_0
Ben Mahmoud, Randa; Chtioui, Hichem; Rigane, Afef. On the prescribed scalar curvature problem on $ {S}^{n}$: The degree zero case. Comptes Rendus. Mathématique, Tome 350 (2012) no. 11-12, pp. 583-586. doi : 10.1016/j.crma.2012.06.012. http://archive.numdam.org/articles/10.1016/j.crma.2012.06.012/
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