The Hodge laplacian on manifolds with boundary

Pierre Guerini; Alessandro Savo

Séminaire de théorie spectrale et géométrie (2002-2003)

  • Volume: 21, page 125-146
  • ISSN: 1624-5458

How to cite

top

Guerini, Pierre, and Savo, Alessandro. "The Hodge laplacian on manifolds with boundary." Séminaire de théorie spectrale et géométrie 21 (2002-2003): 125-146. <http://eudml.org/doc/114471>.

@article{Guerini2002-2003,
author = {Guerini, Pierre, Savo, Alessandro},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {Gallot-Meyer inequality; Chanillo-Treves estimate; absolute boundary conditions; relative boundary conditions; bounding first positive eigenvalue},
language = {eng},
pages = {125-146},
publisher = {Institut Fourier},
title = {The Hodge laplacian on manifolds with boundary},
url = {http://eudml.org/doc/114471},
volume = {21},
year = {2002-2003},
}

TY - JOUR
AU - Guerini, Pierre
AU - Savo, Alessandro
TI - The Hodge laplacian on manifolds with boundary
JO - Séminaire de théorie spectrale et géométrie
PY - 2002-2003
PB - Institut Fourier
VL - 21
SP - 125
EP - 146
LA - eng
KW - Gallot-Meyer inequality; Chanillo-Treves estimate; absolute boundary conditions; relative boundary conditions; bounding first positive eigenvalue
UR - http://eudml.org/doc/114471
ER -

References

top
  1. [A] C. ANNÉ, A note on the generalized Dumbbell problem. Proc.Am. Math. Soc. 123, 8, 2595-2599 ( 1995). Zbl0829.58044MR1257096
  2. [Ch] I. CHAVEL, Eigenvalues in Riemannian geometry. Academic Press, 1984. Zbl0551.53001MR768584
  3. [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. Zbl0709.53031MR1063223
  4. [C-T] S. CHANILLO and F. TREVES, On the lowest eigenvalue of the Hodge Laplacian. J. Diff. Geometry, 45, 273-287 ( 1997) Zbl0874.58087MR1449973
  5. [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. Zbl0636.58036MR932800
  6. [D] J. DODZIUK, Eigenvalues of the Laplacian on forms. Proc. Amer. Math. Society, 85,3 ( 1982). Zbl0502.58038MR656119
  7. [F] L. FRIEDLANDER, Some inequalities between Dirichlet and Neumann eigenvalues. J. Arch. Ration. Mech. Anal. 116, No.2 ( 1991) 153 160. Zbl0789.35124MR1143438
  8. [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. Zbl0316.53036MR454884
  9. [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. Zbl0722.53037MR982334
  10. [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. Zbl0848.53022MR1277111
  11. [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. Zbl1066.58016MR2011982
  12. [G2] R. GUERINI, Prescription du Spectre du Laplacien de Hodge - de Rham. To appear in the Annales Scientifiques de l'École Normale Supérieure. 
  13. [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. Zbl1034.58026MR2020035
  14. [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. Zbl0441.58014MR573435
  15. [McG] J.K. MCGOWAN, The p-spectrum of the Laplacian on compact hyperboïic three manifolds. Math. Ann. 297, 4, 725 745 ( 1993). Zbl0801.53034MR1245416
  16. [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. Zbl0197.18003MR266100
  17. [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. Zbl0073.08203MR84696
  18. [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. Zbl0083.19406MR92431
  19. [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. Zbl0382.53038MR482597
  20. [S] A. SAVO, A mean-value lemma and applications. Bull. Soc. Math. France 129 n. 4 ( 2001) 505-542. Zbl1024.58017MR1894148
  21. [Sc] G. SCHWARZ, Hodge decomposition -A method for solving boundary value problems. Springer. Zbl0828.58002MR1367287
  22. [T] J. TAKAHASHI, On the gap between the first eigenvalues of the Laplacian on functions and 1-forms. Ann. Glob. Anal. Geom. to appear. Zbl1021.58025MR1815136
  23. [W] H.F. WEINBERGER, An isoperimetric inequality for the n-dimensional free membrane problem. J. Rational Mech. Anal. 5 ( 1956) 633-636. Zbl0071.09902MR79286

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.