Spectre conforme et métriques extrémales

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1. [A] ANNE G., Spectre du laplacien et écrasement d'anses, Ann. Scient. Ec. Norm. Sup., 20 ( 1987), 271-280. Zbl0634.58035MR911759
2. [B] BLEECKER D., The Spectrum of a Riemannian manifold with a unit Killing vector field, Trans. Amer. Math. Soc, 275 ( 1983), 409-416. Zbl0506.53021MR678360
3. [BLY] BOURGUIGNON J-P., LI P., YAU S-T., Upper bound for the first eigenvalue of algebraic submanifolds, Comm. Math. Helv., 69 ( 1994), 199-207. Zbl0814.53040MR1282367
4. [CD] COLBOIS B., DODZIUK J., Riemannian metrics with large λ1, Proc. Am. Math. Soc, 122-3 ( 1994), 905-906. Zbl0820.58056MR1213857
5. [CE1] COLBOIS B., EL SOUFI A., Extremal Eigenvalues of the Laplacian in a Conformal Class of Metrics, The "Conformal Spectrum", Armais of Global Analysis and Geometry, 24, ( 2003), 337-349. Zbl1036.58026MR2015867
6. [CE2] COLBOIS B., EL SOUFI A., Eigenvalues of the Laplacian acting on p-forms and metric conformal deformations, à paraître à Proc. Am. Math. Soc. Zbl1095.35013
7. [CV] COLIN DE VERDIÈRE Y., Sur la multiplicité de la première valeur propre non nulle du laplacien, Comment. Math. Helvetici, 61 ( 1986), 254-270. Zbl0607.53028MR856089
8. [EI1] EL SOUFI A., ILIAS S., Le volume conforme et ses applications d'après Li et Yau, Sémin. Théor. Spectrale Géom., Institut Fourier, année 1983-1984, NoVII, ( 1984). Zbl0757.53028
9. [EI2] EL SOUFI A., ILIAS S., Immersion minimales, première valeur propre du laplacien et volume conforme, Math. Ann., 275 ( 1986), 257-267. Zbl0675.53045MR854009
10. [EI3] EL SOUFI A., ILIAS S., Extremal metrics for the λ1 functional in a conformal class, Proc. Am. Math. Soc, 131-5( 2003), 1611-1618. Zbl1027.58010MR1950293
11. [FN] FRIEDLANDER L., NADIRASHVILI N., A differential invariant related to the first eigenvalue of the Laplacian, Int. Math. Res. Not., 17, ( 1999), 939-952. Zbl0941.58019MR1717641
12. [GP] GENTILE G., PAGLIARA V., Riemannian metrics with large first eigenvalue on forms of degre p, Proc. Am. Math. Soc, 123-12 ( 1995), 3855-3858. Zbl0848.53022MR1277111
13. [H] HERSCH J., Quatre propriétés isopérimétriques des membranes sphériques homogènes, C. R. Acad. Sc. Paris, Série A, 270 ( 1970), 1645-1648. Zbl0224.73083MR292357
14. [JNP] JAKOBSON D., NADIRASHVILI N., POLTEROVICH I., Extremal Metric for the First Eigenvalue on a Klein Boule, Preprint 2003. 
15. [K] KOREVAAR N., Upper bounds for eigenvalues of conformal metrics. J. Differ. Geom., 37-1 ( 1993), 73-93. Zbl0794.58045MR1198600
16. [LY] LI P., YAU S.T., A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Invent Math., 69, ( 1982), 269-291. Zbl0503.53042MR674407
17. [M] MUTO H., The first eigenvalue of the Laplacian on even dimensional spheres, Tohoku Math. J., 32 ( 1980), 427-432. Zbl0427.53020MR590038
18. [N1] NADIRASHVIH N., Berger's isoperimetric problem and minimal immersions of surfaces, GAFA, 6 ( 1996), 877-897. Zbl0868.58079MR1415764
19. [N2] NADIRASHVILI N., Isoperimetric inequality for the second eigenvalue of a sphere, J. Differential Geom., 61 ( 2002), 335-340. Zbl1071.58024MR1972149
20. [P] POLTEROVICH L, Symplectic aspects of the first eigenvalue, J. Reine Angew. Math., 502 ( 1998),?-17. Zbl0902.58012MR1647622
21. [T] TAKAHASHI J., Collapsing of connected sums and the eigenvalues of the Laplacian, J. Geom. Phys., 40, 201-208. ( 2002) Zbl1034.58027MR1866987
22. [Y] YAU S.T., Problem section. Seminar in differential geometry, Ann. Math. Stud., 102 ( 1982), 669-706. Zbl0479.53001MR645762
23. [YY] YANG E., YAU S .T., Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds, Ann. Scuola Norm. Sup.Pisa, 7 ( 1980), 55-63. Zbl0446.58017MR577325

1. Pierre Jammes, Extrema de valeurs propres dans une classe conforme