Topological tools for the prescribed scalar curvature problem on S n

Dina Abuzaid; Randa Ben Mahmoud; Hichem Chtioui; Afef Rigane

Open Mathematics (2014)

  • Volume: 12, Issue: 12, page 1829-1839
  • ISSN: 2391-5455

Abstract

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In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

How to cite

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Dina Abuzaid, et al. "Topological tools for the prescribed scalar curvature problem on S n." Open Mathematics 12.12 (2014): 1829-1839. <http://eudml.org/doc/269413>.

@article{DinaAbuzaid2014,
abstract = {In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].},
author = {Dina Abuzaid, Randa Ben Mahmoud, Hichem Chtioui, Afef Rigane},
journal = {Open Mathematics},
keywords = {Scalar curvature; Variational method; β-flatness condition; Loss of compactness; Critical points at infinity; Topological method; scalar curvature; variational method; -flatness condition; loss of compactness; critical points at infinity; topological method},
language = {eng},
number = {12},
pages = {1829-1839},
title = {Topological tools for the prescribed scalar curvature problem on S n},
url = {http://eudml.org/doc/269413},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Dina Abuzaid
AU - Randa Ben Mahmoud
AU - Hichem Chtioui
AU - Afef Rigane
TI - Topological tools for the prescribed scalar curvature problem on S n
JO - Open Mathematics
PY - 2014
VL - 12
IS - 12
SP - 1829
EP - 1839
AB - In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].
LA - eng
KW - Scalar curvature; Variational method; β-flatness condition; Loss of compactness; Critical points at infinity; Topological method; scalar curvature; variational method; -flatness condition; loss of compactness; critical points at infinity; topological method
UR - http://eudml.org/doc/269413
ER -

References

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  8. [8] R. Ben Mahmoud, H. Chtioui, Prescribing the Scalar Curvature Problem on Higher-Dimensional Manifolds, Discrete and Continuous Dynamical Systems A, 32 (2012), 1857–1879. http://dx.doi.org/10.3934/dcds.2012.32.1857 Zbl1242.58006
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