Geodesic
Multiplicity results for the prescribed scalar curvature on low spheres
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 4, pp. 609-634

Voir la notice de l'article provenant de la source Numdam

In this paper, we consider the problem of multiplicity of conformal metrics of prescribed scalar curvature on standard spheres 𝕊 3 ,𝕊 4 . Under generic conditions we establish some Morse Inequalities at Infinity, which give a lower bound on the number of solutions to the above problem in terms of the total contribution of its critical points at Infinity to the difference of topology between the level sets of the associated Euler-Lagrange functional. As a by-product of our arguments we derive a new existence result on 𝕊 4 through an Euler-Hopf type formula.

Classification : 58E05, 35J65, 53C21, 35B40 
@article{ASNSP_2008_5_7_4_609_0,
     author = {Ben Ayed, Mohamed and Ould Ahmedou, Mohameden},
     title = {Multiplicity results for the prescribed scalar curvature on low spheres},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {609--634},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 7},
     number = {4},
     year = {2008},
     mrnumber = {2483638},
     zbl = {1213.58009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_4_609_0/}
}
TY  - JOUR
AU  - Ben Ayed, Mohamed
AU  - Ould Ahmedou, Mohameden
TI  - Multiplicity results for the prescribed scalar curvature on low spheres
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2008
SP  - 609
EP  - 634
VL  - 7
IS  - 4
PB  - Scuola Normale Superiore, Pisa
UR  - http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_4_609_0/
LA  - en
ID  - ASNSP_2008_5_7_4_609_0
ER  - 
%0 Journal Article
%A Ben Ayed, Mohamed
%A Ould Ahmedou, Mohameden
%T Multiplicity results for the prescribed scalar curvature on low spheres
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2008
%P 609-634
%V 7
%N 4
%I Scuola Normale Superiore, Pisa
%U http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_4_609_0/
%G en
%F ASNSP_2008_5_7_4_609_0
Ben Ayed, Mohamed; Ould Ahmedou, Mohameden. Multiplicity results for the prescribed scalar curvature on low spheres. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 4, pp. 609-634. http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_4_609_0/