Prescribing scalar curvature on S 3

Matthias Schneider

Annales de l'I.H.P. Analyse non linéaire (2007)

  • Volume: 24, Issue: 4, page 563-587
  • ISSN: 0294-1449

How to cite

top

Schneider, Matthias. "Prescribing scalar curvature on ${S}^{3}$." Annales de l'I.H.P. Analyse non linéaire 24.4 (2007): 563-587. <http://eudml.org/doc/78750>.

@article{Schneider2007,
author = {Schneider, Matthias},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {prescribed scalar curvature; Leray-Schauder degree; finite dimensional reduction},
language = {eng},
number = {4},
pages = {563-587},
publisher = {Elsevier},
title = {Prescribing scalar curvature on $\{S\}^\{3\}$},
url = {http://eudml.org/doc/78750},
volume = {24},
year = {2007},
}

TY - JOUR
AU - Schneider, Matthias
TI - Prescribing scalar curvature on ${S}^{3}$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 4
SP - 563
EP - 587
LA - eng
KW - prescribed scalar curvature; Leray-Schauder degree; finite dimensional reduction
UR - http://eudml.org/doc/78750
ER -

References

top
  1. [1] Ambrosetti A., Badiale M., Homoclinics: Poincaré–Melnikov type results via a variational approach, Ann. Inst. H. Poincaré Anal. Non Linéaire15 (2) (1998) 233-252. Zbl1004.37043
  2. [2] Ambrosetti A., Garcia Azorero J., Peral I., Perturbation of Δ u + u ( N + 2 ) / ( N - 2 ) = 0 , the scalar curvature problem in R N , and related topics, J. Funct. Anal.165 (1) (1999) 117-149. Zbl0938.35056MR1696454
  3. [3] Aubin T., Some Nonlinear Problems in Riemannian Geometry, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. Zbl0896.53003MR1636569
  4. [4] Aubin T., Bahri A., Une hypothèse topologique pour le problème de la courbure scalaire prescrite, J. Math. Pures Appl. (9)76 (10) (1997) 843-850. Zbl0916.58041MR1489940
  5. [5] Bahri A., Coron J.-M., The scalar-curvature problem on the standard three-dimensional sphere, J. Funct. Anal.95 (1) (1991) 106-172. Zbl0722.53032MR1087949
  6. [6] Bianchi G., Non-existence and symmetry of solutions to the scalar curvature equation, Comm. Partial Differential Equations21 (1–2) (1996) 229-234. Zbl0844.35025
  7. [7] Bourguignon J.-P., Ezin J.-P., Scalar curvature functions in a conformal class of metrics and conformal transformations, Trans. Amer. Math. Soc.301 (2) (1987) 723-736. Zbl0622.53023MR882712
  8. [8] Brezis H., Kato T., Remarks on the Schrödinger operator with singular complex potentials, J. Math. Pures Appl. (9)58 (2) (1979) 137-151. Zbl0408.35025MR539217
  9. [9] Caffarelli L.A., Gidas B., Spruck J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math.42 (3) (1989) 271-297. Zbl0702.35085MR982351
  10. [10] Chang S.-Y.A., Gursky M.J., Yang P.C., The scalar curvature equation on 2- and 3-spheres, Calc. Var. Partial Differential Equations1 (2) (1993) 205-229. Zbl0822.35043MR1261723
  11. [11] Chen C.-C., Lin C.-S., Prescribing scalar curvature on S N . I. A priori estimates, J. Differential Geom.57 (1) (2001) 67-171. Zbl1043.53028MR1871492
  12. [12] Chen W., Li C., Prescribing scalar curvature on S n , Pacific J. Math.199 (1) (2001) 61-78. Zbl1060.53047MR1847147
  13. [13] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in R n , in: Mathematical Analysis and Applications, Part A, Adv. in Math. Suppl. Stud., vol. 7, Academic Press, New York, 1981, pp. 369-402. Zbl0469.35052MR634248
  14. [14] Kazdan J.L., Warner F.W., Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures, Ann. of Math. (2)101 (1975) 317-331. Zbl0297.53020MR375153
  15. [15] Li Y.Y., Prescribing scalar curvature on S n and related problems. I, J. Differential Equations120 (2) (1995) 319-410. Zbl0827.53039MR1347349
  16. [16] Li Y.Y., Prescribing scalar curvature on S n and related problems. II. Existence and compactness, Comm. Pure Appl. Math.49 (6) (1996) 541-597. Zbl0849.53031MR1383201
  17. [17] M. Schneider, A priori estimates for the prescribed scalar curvature equation on S 3 , preprint, 2004. 
  18. [18] Schoen R., Zhang D., Prescribed scalar curvature on the n-sphere, Calc. Var. Partial Differential Equations4 (1) (1996) 1-25. Zbl0843.53037MR1379191

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.