On the Sobolev constant and the p -spectrum of a compact riemannian manifold

Peter Li

Annales scientifiques de l'École Normale Supérieure (1980)

  • Volume: 13, Issue: 4, page 451-468
  • ISSN: 0012-9593

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Li, Peter. "On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold." Annales scientifiques de l'École Normale Supérieure 13.4 (1980): 451-468. <http://eudml.org/doc/82061>.

@article{Li1980,
author = {Li, Peter},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Sobolev constant; isoperimetric constant; Laplacian on forms; eigenvalues and multiplicities; Ricci curvature},
language = {eng},
number = {4},
pages = {451-468},
publisher = {Elsevier},
title = {On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold},
url = {http://eudml.org/doc/82061},
volume = {13},
year = {1980},
}

TY - JOUR
AU - Li, Peter
TI - On the Sobolev constant and the $p$-spectrum of a compact riemannian manifold
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1980
PB - Elsevier
VL - 13
IS - 4
SP - 451
EP - 468
LA - eng
KW - Sobolev constant; isoperimetric constant; Laplacian on forms; eigenvalues and multiplicities; Ricci curvature
UR - http://eudml.org/doc/82061
ER -

References

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  1. [1] E. BOMBIERI, Theory of Minimal Surfaces and a Counter-Example to the Bernstein Conjecture in High Dimension (Lecture Notes, Courant Institute, 1970). 
  2. [2] J. CHEEGER, A Lower Bound for the Smallest Eigenvalue of the Laplacian in Problem in Analysis, a Symposium in honor of S. Bochner, Princeton University Press, Princeton, 1970. Zbl0212.44903
  3. [3] S. Y. CHENG, Eigenfunctions and Nodal Sets (Comment Math. Helv., Vol. 51, 1976, pp. 43-55). Zbl0334.35022MR53 #1661
  4. [4] C. CROKE, Some Isoperimetric Inequalities and Consequences (Ann. scient. Éc. Norm. Sup., (4), T. 13, 1980, pp. 419-435). Zbl0465.53032MR83d:58068
  5. [5] S. GALLOT and D. MEYER, Operateur de courbure et laplacien des formes différentielles d'une variété riemannienne (J. Math. pures et appl., Vol. 54, 1975, pp. 259-284). Zbl0316.53036MR56 #13128
  6. [6] M. GROMOV, Manifolds of Negative Curvature (preprint). 
  7. [7] R. OSSERMAN, The Isoperimetric Inequality (Bulletin A.M.S., Vol. 84, No. 6, 1978, pp. 1182-1238). Zbl0411.52006MR58 #18161
  8. [8] S. T. YAU, Isoperimetric Constants and the First Eigenvalue of a Compact Riemannian Manifold (Ann. scient. Éc. Norm. Sup., Vol. 4, t. 8, 1975, pp. 487-507). Zbl0325.53039MR53 #1478

Citations in EuDML Documents

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  1. Min-Oo, An L 2 -isolation theorem for Yang-Mills fields
  2. J. Dodziuk, Min-Oo, An L 2 -isolation theorem for Yang-Mills fields over complete manifolds
  3. Saïd Ilias, Constantes explicites pour les inégalités de Sobolev sur les variétés riemanniennes compactes
  4. Christopher B. Croke, Some isoperimetric inequalities and eigenvalue estimates
  5. Toshiaki Adachi, Toshikazu Sunada, Energy spectrum of certain harmonic mappings
  6. P. Bérard, S. Gallot, Inégalités isopérimétriques pour l'équation de la chaleur et application à l'estimation de quelques invariants
  7. Bruno Colbois, Gilles Courtois, Petites valeurs propres et classe d’Euler des S 1 - fibrés
  8. Peter Buser, A note on the isoperimetric constant
  9. Sylvestre Gallot, Finiteness theorems with integral conditions on curvature
  10. S. Gallot, D. Meyer, D'un résultat hilbertien à un principe de comparaison entre spectres. Applications

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