Existence results for the prescribed Scalar curvature on S 3

Randa Ben Mahmoud[1]; Hichem Chtioui

  • [1] Faculté des Sciences de Sfax Département de Mathématiques Route Soukra 3018 Sfax (Tunisie)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 3, page 971-986
  • ISSN: 0373-0956

Abstract

top
This paper is devoted to the existence of conformal metrics on S 3 with prescribed scalar curvature. We extend well known existence criteria due to Bahri-Coron.

How to cite

top

Mahmoud, Randa Ben, and Chtioui, Hichem. "Existence results for the prescribed Scalar curvature on $S^{3}$." Annales de l’institut Fourier 61.3 (2011): 971-986. <http://eudml.org/doc/219831>.

@article{Mahmoud2011,
abstract = {This paper is devoted to the existence of conformal metrics on $S^\{3\}$ with prescribed scalar curvature. We extend well known existence criteria due to Bahri-Coron.},
affiliation = {Faculté des Sciences de Sfax Département de Mathématiques Route Soukra 3018 Sfax (Tunisie)},
author = {Mahmoud, Randa Ben, Chtioui, Hichem},
journal = {Annales de l’institut Fourier},
keywords = {Scalar curvature; critical points at infinity; topological method; scalar curvature},
language = {eng},
number = {3},
pages = {971-986},
publisher = {Association des Annales de l’institut Fourier},
title = {Existence results for the prescribed Scalar curvature on $S^\{3\}$},
url = {http://eudml.org/doc/219831},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Mahmoud, Randa Ben
AU - Chtioui, Hichem
TI - Existence results for the prescribed Scalar curvature on $S^{3}$
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 3
SP - 971
EP - 986
AB - This paper is devoted to the existence of conformal metrics on $S^{3}$ with prescribed scalar curvature. We extend well known existence criteria due to Bahri-Coron.
LA - eng
KW - Scalar curvature; critical points at infinity; topological method; scalar curvature
UR - http://eudml.org/doc/219831
ER -

References

top
  1. T. Aubin, Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. Pures et Appl. 55 (1976), 269-296 Zbl0336.53033MR431287
  2. T. Aubin, A. Bahri, Une hypothèse topologique pour le problème de la courbure scalaire prescrite. (French) [A topological hypothesis for the problem of prescribed scalar curvature], J. Math. Pures Appl. 76 (1997), 843-850 Zbl0916.58041MR1489940
  3. A. Bahri, Critical point at infinity in some variational problems, 182 (1989), Longman Sci. Tech., Harlow Zbl0676.58021MR1019828
  4. A. Bahri, An invariant for yamabe-type flows with applications to scalar curvature problems in high dimensions, A celebration of J. F. Nash Jr., Duke Math. J. 81 (1996), 323-466 Zbl0856.53028MR1395407
  5. A. Bahri, J. M. Coron, The scalar curvature problem on the standard three dimensional spheres, J. Funct. Anal. 95 (1991), 106-172 Zbl0722.53032MR1087949
  6. A. Bahri, P. Rabinowitz, Periodic orbits of hamiltonian systems of three body type, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991), 561-649 Zbl0745.34034MR1145561
  7. M. Ben Ayed, Y. Chen, H. Chtioui, M. Hammami, On the prescribed scalar curvature problem on 4-manifolds, Duke Math. J. 84 (1996), 633-677 Zbl0862.53034MR1408540
  8. S. A. Chang, M. J. Gursky, P. C. Yang, The scalar curvature equation on 2 and 3 spheres, Calc. Var. 1 (1993), 205-229 Zbl0822.35043MR1261723
  9. S. Y. Chang, P. Yang, A perturbation result in prescribing scalar curvature on S n , Duke Math. J. 64 (1991), 27-69 Zbl0739.53027MR1131392
  10. C. C. Chen, C. S. Lin, Prescribing scalar curvature on S n , Part I: Apriori estimates, J. differential geometry 57 (2001), 67-171 Zbl1043.53028MR1871492
  11. H. Chtioui, Prescribing the Scalar Curvature Problem on Three and Four Manifolds, Advanced Nonlinear Studies 3 (2003), 457-470 Zbl1051.53031MR2017242
  12. C. C. Conley, Isolated invariant sets and the Morse index, 38 (1978), AMS Zbl0397.34056MR511133
  13. J. Escobar, R. Schoen, Conformal metrics with prescribed scalar curvature, Inventiones Math. 86 (1986), 243-254 Zbl0628.53041MR856845
  14. A. Floer, Cuplength Estimates on Lagrangian intersections, Comm. Pure and Applied Math XLII (1989), 335-356 Zbl0683.58017MR990135
  15. J. Kazdan, J. Warner, Existence and conformal deformations of metrics with prescribed Gaussian and scalar curvature, Annals of Math. 101 (1975), 317-331 Zbl0297.53020MR375153
  16. Y. Y. Li, Prescribing scalar curvature on S 3 , S 4 and related problems, J. Functional Analysis 118 (1993), 43-118 Zbl0790.53040MR1245597
  17. Y. Y. Li, Prescribing scalar curvature on S n and related topics, Part I, Journal of Differential Equations 120 (1995), 319-410 Zbl0827.53039MR1347349
  18. Y. Y. Li, Prescribing scalar curvature on S n and related topics, Part II: existence and compactness, Comm. Pure Appl. Math. 49 (1996), 541-579 Zbl0849.53031MR1383201
  19. C. S. Lin, On Liouville theorem and apriori estimates for the scalar curvature equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci 4 (1998), 107-130 Zbl0974.53032MR1658881
  20. P. L. Lions, The concentration compactness principle in the calculus of variations. The limit case, Rev. Mat. Iberoamericana 1 (1985), I: 165-201, II: 45–121 Zbl0704.49006MR850686
  21. J. Milnor, Lectures on the h-cobordism theorem, (1965), Princeton University Press Zbl0161.20302MR190942
  22. R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), 479-495 Zbl0576.53028MR788292
  23. R. Schoen, D. Zhang, Prescribed scalar curvature on the n-sphere, Calculus of Variations and Partial Differential Equations 4 (1996), 1-25 Zbl0843.53037MR1379191
  24. M. Struwe, A global compactness result for elliptic boundary value problem involving limiting nonlinearities, Math. Z. 187 (1984), 511-517 Zbl0535.35025MR760051

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.