Prescription du spectre du laplacien de Hodge–de Rham
Annales scientifiques de l'École Normale Supérieure (2004)
- Volume: 37, Issue: 2, page 270-303
- ISSN: 0012-9593
Access Full Article
topHow to cite
topGuerini, Pierre. "Prescription du spectre du laplacien de Hodge–de Rham." Annales scientifiques de l'École Normale Supérieure 37.2 (2004): 270-303. <http://eudml.org/doc/82631>.
@article{Guerini2004,
author = {Guerini, Pierre},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {convergence of spectrum; Laplacian; Euclidean domain},
language = {fre},
number = {2},
pages = {270-303},
publisher = {Elsevier},
title = {Prescription du spectre du laplacien de Hodge–de Rham},
url = {http://eudml.org/doc/82631},
volume = {37},
year = {2004},
}
TY - JOUR
AU - Guerini, Pierre
TI - Prescription du spectre du laplacien de Hodge–de Rham
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2004
PB - Elsevier
VL - 37
IS - 2
SP - 270
EP - 303
LA - fre
KW - convergence of spectrum; Laplacian; Euclidean domain
UR - http://eudml.org/doc/82631
ER -
References
top- [1] Anné C., Spectre du Laplacien et écrasement d'anses, Ann. Sci. Éc. Norm. Sup.20 (1987) 271-280. Zbl0634.58035MR911759
- [2] Anné C., A note on the generalized Dumbbell problem, Proc. Amer Math. Soc.123 (8) (1995) 2595-2599. Zbl0829.58044MR1257096
- [3] Anné C., Colbois B., Opérateur de Hodge–Laplace sur les variétés compactes privées d'un nombre fini de boules, J. Funct. Anal.115 (1) (1993). Zbl0791.58018MR1228148
- [4] Anné C., Colbois B., Spectre du Laplacien agissant sur les p-formes différentielles et écrasement d'anses, Math. Ann.303 (3) (1995) 545-573. Zbl0909.58054MR1355003
- [5] Ashbaugh M.S., Benguria R.D., Proof of the Payne–Polya–Weinberger conjecture, Bull. Amer. Math. Soc., New Ser.25 (1) (1991) 19-29. Zbl0736.35075MR1085824
- [6] Bérard P., Spectral Geometry : Direct and Inverse Problem, in: Lecture Notes in Maths., vol. 1207, Springer, Berlin, 1986. Zbl0608.58001MR861271
- [7] Cheeger J., On the Hodge theory of Riemannian manifolds, in: Osserman R., Weinstein A. (Eds.), Geometry of the Laplace Operator, Proceedings of Symposia in Pure Mathematics, vol. 36, 1980, pp. 91-146. Zbl0461.58002MR573430
- [8] Cheeger J., Spectral geometry of Riemannian singular spaces, J. Differential Geom.18 (1983) 575-657. Zbl0529.58034MR730920
- [9] Colbois B., Dodziuk J., Riemannian metrics with large λ1, Proc. Amer. Math. Soc.122 (3) (1994). Zbl0820.58056
- [10] Colin de Verdière Y., Construction de laplaciens dont une partie finie du spectre est donnée, Ann. Scient. Éc. Norm. Sup., 420 (1987) 599-615. Zbl0636.58036MR932800
- [11] Colin de Verdière Y., Spectres de Graphes, Cours spécialisé, vol. 4, Soc. Math. de France, 1998. Zbl0913.05071MR1652692
- [12] Courtois G., Comportement du spectre d'une variété riemannienne compacte sous perturbation topologique par excision d'un domaine, Thèse, Institut Fourier, Grenoble, 1987.
- [13] Dodziuk J., Eigenvalues of the Laplacian on forms, Proc. Amer. Math. Soc.85 (1982) 3. Zbl0502.58038MR656119
- [14] Dodziuk J., Appendix of “Eigenvalues in Riemannian Geometry”, Chavel, Academic Press, Orlando, 1984.
- [15] Dodziuk J., Mc Gowan J.K., The spectrum of the Hodge Laplacian for a degenerating family of hyperbolic three manifolds, Trans. Amer. Math. Soc.347 (1995) 1981-1995. Zbl0849.58069MR1308007
- [16] Gallot S., Hulin D., Lafontaine J., Riemannian Geometry, Springer-Verlag, 1997. Zbl0636.53001
- [17] Guerini P., Spectre du Laplacien agissant sur les formes différentielles d'un domaine euclidien, Thèse de doctorat, Université de Savoie, 2001.
- [18] Guerini P., Spectre du Laplacien de Hodge–de Rham : estimées sur les variétés convexes, À paraître dans le Bulletin of the London Mathematical Society. Zbl1066.58016
- [19] Gentile G., Pagliara V., Riemannian metrics with large first eigenvalue on forms of degree p, Proc. Amer. Math. Soc.123 (12) (1995) 3855-3858. Zbl0848.53022MR1277111
- [20] Lohkamp J., Discontinuity of geometric expansions, Comment. Math. Helvetia71 (1996) 213-228. Zbl0857.58041MR1396673
- [21] Mc Gowan J.K., The p-spectrum of the Laplacian on compact hyperbolic three manifolds, Math. Ann.297 (4) (1993) 725-745. Zbl0801.53034MR1245416
- [22] Payne L., Pólya G., Weinberger H., On the ratio of consecutive eigenvalues, J. Math. Phys.35 (1956) 289-298. Zbl0073.08203MR84696
- [23] Taylor M.E., Partial Differential Equations, in: Basic Theory (vol. 1), Texts in Applied Mathematics, vol. 115, Springer, 1996. Zbl0869.35001MR1395148
- [24] Weinberger H.F., An isoperimetric inequality for the n-dimensional free membrane problem, J. Rational Mech. Anal.5 (1956) 633-636. Zbl0071.09902MR79286
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.