Multiplicity results for the prescribed scalar curvature on low spheres

Mohamed Ben Ayed; Mohameden Ould Ahmedou

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)

  • Volume: 7, Issue: 4, page 609-634
  • ISSN: 0391-173X

Abstract

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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 someMorse 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 Infinityto 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.

How to cite

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Ben Ayed, Mohamed, and Ould Ahmedou, Mohameden. "Multiplicity results for the prescribed scalar curvature on low spheres." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.4 (2008): 609-634. <http://eudml.org/doc/272288>.

@article{BenAyed2008,
abstract = {In this paper, we consider the problem of multiplicity of conformal metrics of prescribed scalar curvature on standard spheres $\mathbb \{S\}^3, \mathbb \{S\}^4$. Under generic conditions we establish someMorse 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 Infinityto 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 $\mathbb \{S\}^4$ through an Euler-Hopf type formula.},
author = {Ben Ayed, Mohamed, Ould Ahmedou, Mohameden},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {multiplicity of conformal metrics; prescribed scalar curvature; spheres; Morse inequalities at infinity; critical points at infinity},
language = {eng},
number = {4},
pages = {609-634},
publisher = {Scuola Normale Superiore, Pisa},
title = {Multiplicity results for the prescribed scalar curvature on low spheres},
url = {http://eudml.org/doc/272288},
volume = {7},
year = {2008},
}

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
PB - Scuola Normale Superiore, Pisa
VL - 7
IS - 4
SP - 609
EP - 634
AB - In this paper, we consider the problem of multiplicity of conformal metrics of prescribed scalar curvature on standard spheres $\mathbb {S}^3, \mathbb {S}^4$. Under generic conditions we establish someMorse 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 Infinityto 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 $\mathbb {S}^4$ through an Euler-Hopf type formula.
LA - eng
KW - multiplicity of conformal metrics; prescribed scalar curvature; spheres; Morse inequalities at infinity; critical points at infinity
UR - http://eudml.org/doc/272288
ER -

References

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