Multiplicity results for the prescribed scalar curvature on low spheres

Autor:	Mohameden Ould Ahmedou, Mohamed Ben Ayed
Rok vydání:	2009
Předmět:	Pure mathematics Mathematics (miscellaneous) Prescribed scalar curvature problem Multiplicity results Conformal map SPHERES Multiplicity (mathematics) Topology Upper and lower bounds Theoretical Computer Science Mathematics Scalar curvature
Zdroj:	ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :609-634
ISSN:	2036-2145 0391-173X
DOI:	10.2422/2036-2145.2008.4.02
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::02b3b03832a4aef08b34b52c90d9bb80 https://doi.org/10.2422/2036-2145.2008.4.02