The Hodge laplacian on manifolds with boundary
Séminaire de théorie spectrale et géométrie, Tome 21 (2002-2003), pp. 125-146. 
@article{TSG_2002-2003__21__125_0,
     author = {Pierre Guerini and Alessandro Savo},
     title = {The {Hodge} laplacian on manifolds with boundary},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {125--146},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {21},
     year = {2002-2003},
     doi = {10.5802/tsg.338},
     zbl = {1050.58025},
     mrnumber = {2052829},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.338/}
}
TY  - JOUR
AU  - Pierre Guerini
AU  - Alessandro Savo
TI  - The Hodge laplacian on manifolds with boundary
JO  - Séminaire de théorie spectrale et géométrie
PY  - 2002-2003
SP  - 125
EP  - 146
VL  - 21
PB  - Institut Fourier
PP  - Grenoble
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.338/
DO  - 10.5802/tsg.338
LA  - en
ID  - TSG_2002-2003__21__125_0
ER  - 
%0 Journal Article
%A Pierre Guerini
%A Alessandro Savo
%T The Hodge laplacian on manifolds with boundary
%J Séminaire de théorie spectrale et géométrie
%D 2002-2003
%P 125-146
%V 21
%I Institut Fourier
%C Grenoble
%U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.338/
%R 10.5802/tsg.338
%G en
%F TSG_2002-2003__21__125_0
Pierre Guerini; Alessandro Savo. The Hodge laplacian on manifolds with boundary. Séminaire de théorie spectrale et géométrie, Tome 21 (2002-2003), pp. 125-146. doi : 10.5802/tsg.338. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.338/

[A] C. Anné, A note on the generalized Dumbbell problem. Proc.Am. Math. Soc. 123, 8, 2595-2599 ( 1995). | MR | Zbl

[Ch] I. Chavel, Eigenvalues in Riemannian geometry. Academic Press, 1984. | MR | Zbl

[C-C] B. Colbois and G. Courtois, A note on the first eigenvalue of the Laplacian acting on p-forms ManuscriptaMath. 68 ( 1990) 143-160. | MR | Zbl

[C-T] S. Chanillo and F. Treves, On the lowest eigenvalue of the Hodge Laplacian. J. Diff. Geometry, 45, 273-287 ( 1997) | MR | Zbl

[CV] Y. Colin De Verdière, Construction de laplaciens dont une partie finie du spectre est donnée.Ann. Scient. Ec. Norm. Sup., 4e série, t. 20, ( 1987), 599 615. | Numdam | MR | Zbl

[D] J. Dodziuk, Eigenvalues of the Laplacian on forms. Proc. Amer. Math. Society, 85,3 ( 1982). | MR | Zbl

[F] L. Friedlander, Some inequalities between Dirichlet and Neumann eigenvalues. J. Arch. Ration. Mech. Anal. 116, No.2 ( 1991) 153 160. | MR | Zbl

[G M1] S. Gallot and D. Meyer, Operateur de courbure et Laplacien des formes differentielles d'une variété riemannienne J. Math. PuresAppl. 54 ( 1975) 259 284. | MR | Zbl

[G-M2] S. Gallot and D. Meyer, D'un résultat hilbertien à un principe de comparaison entre spectres. Applications. Ann. Scient. Ec. Norm. Sup., 4 Serie, t. 21 ( 1988) 561-591. | Numdam | MR | Zbl

[G-P] G. Gentile and V. Pagliara, Riemannian metrics with large first eigenvalue on forms of degree p. Proc. Amer. Math. Soc. 123 ( 1995) no 12, 3855 3858. | MR | Zbl

[G1] P. Guerini, Spectre du Lapladen de Hodge - de Rham: Estimées sur les Variétés Convexes. To appear in the Bulletin of the London Mathematical Society. | MR | Zbl

[G2] R. Guerini, Prescription du Spectre du Laplacien de Hodge - de Rham. To appear in the Annales Scientifiques de l'École Normale Supérieure. | EuDML | Numdam | MR

[G-S] P. Guerini and A. Savo, Eigenvalues and gap estimâtes for the Laplacian acting on p-forms. To appear in the Transactions of the American Mathematical Society. | MR | Zbl

[L-Y] P. Li and S-T. Yau, Estimates of eigenvalues of a compact Riemannian manifold. Proc. Symp. Pure Math. t. 36 ( 1980) 205-239. | MR | Zbl

[McG] J.K. Mcgowan, The p-spectrum of the Laplacian on compact hyperboïic three manifolds. Math. Ann. 297, 4, 725 745 ( 1993). | EuDML | MR | Zbl

[McK] H.P. Mckean, An upper bound for the spectrum of Δ on a manifold of negative curvature. J. Diff. Geom. 4( 1970)359-366. | MR | Zbl

[P-P-W] L. Payne, G. Pólya, H. Weinberger, On the Ratio of Consecutive Eigenvalues. J. of Math. and Phys., vol 35, ( 1956), 289-298. | MR | Zbl

[P-W] L. Payne and H. Weinberger, Lower bounds for vibration frequencies of elastically supportes membranes and plates. J. Soc. Ind. Appl. Math. 5 ( 1957) 171-182. | MR | Zbl

[R] R.C. Reilly, On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space. Comment. Math. Helv. 52 n. 4 ( 1977) 525-533. | EuDML | MR | Zbl

[S] A. Savo, A mean-value lemma and applications. Bull. Soc. Math. France 129 n. 4 ( 2001) 505-542. | EuDML | Numdam | MR | Zbl

[Sc] G. Schwarz, Hodge decomposition -A method for solving boundary value problems. Springer. | MR | Zbl

[T] J. Takahashi, On the gap between the first eigenvalues of the Laplacian on functions and 1-forms. Ann. Glob. Anal. Geom. to appear. | MR | Zbl

[W] H.F. Weinberger, An isoperimetric inequality for the n-dimensional free membrane problem. J. Rational Mech. Anal. 5 ( 1956) 633-636. | MR | Zbl

Cité par Sources :