Isoperimetric constants and the first eigenvalue of a compact riemannian manifold

Shing-Tung Yau

Annales scientifiques de l'École Normale Supérieure (1975)

  • Volume: 8, Issue: 4, page 487-507
  • ISSN: 0012-9593

How to cite

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Yau, Shing-Tung. "Isoperimetric constants and the first eigenvalue of a compact riemannian manifold." Annales scientifiques de l'École Normale Supérieure 8.4 (1975): 487-507. <http://eudml.org/doc/81968>.

@article{Yau1975,
author = {Yau, Shing-Tung},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {4},
pages = {487-507},
publisher = {Elsevier},
title = {Isoperimetric constants and the first eigenvalue of a compact riemannian manifold},
url = {http://eudml.org/doc/81968},
volume = {8},
year = {1975},
}

TY - JOUR
AU - Yau, Shing-Tung
TI - Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1975
PB - Elsevier
VL - 8
IS - 4
SP - 487
EP - 507
LA - eng
UR - http://eudml.org/doc/81968
ER -

References

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  2. [2] R. BISHOP and R. CRISTTENDEN, Geometry of Manifolds, Academic Press, 1964. Zbl0132.16003
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  4. [4] I. CHAVEL and E. FELDMAN, The First Eigenvalue of the Laplacian on Manifolds of Non-Negative Curvature (to appear). Zbl0291.53021
  5. [5] J. CHEEGER, The Relation Between the Laplacian and the Diameter for Manifolds of Non-Negative Curvature (Arch. der Math., Vol. 19, 1968, p. 558-560). Zbl0177.50201MR38 #6503
  6. [6] J. CHEEGER, A Lower Bound for the Smallest Eigenvalue of the Laplacian, In “Problems in Analysis, a symposium in honor of S. Bochner”, Princeton University Press, 1970. Zbl0212.44903
  7. [7] S. Y. CHENG, Eigenfunctions and Eigenvalues of Laplacian (to ppear in the Proceedings of Symposium on Differential Geometry). Zbl0308.35076
  8. [8] S. Y. CHENG, Eigenvalue Comparison Theorems and its Geometric Applications (Math. Z., Vol. 143, 1975, p. 289-297.) Zbl0329.53035MR51 #14170
  9. [9] L. KEEN, Collars on Riemann Surfaces, In “Discontinuous Groups and Riemann Surfaces”, edited by by GREENBERG, Princeton University Press, 1974, p. 263-268. Zbl0304.30014MR52 #738
  10. [10] A. HUBER, On the Isoperimetric Inequality on Surfaces of Variable Gaussian Curvature (Ann. of Math., Vol. 60, 1954, p. 237-247). Zbl0056.15801MR16,508d
  11. [11] J. HERSCH, Caractérisation variationnelle d'une somme de valeurs propres consécutives (C. R. Acad. Sc., t. 252, 1961, série A, p. 1714-1716). Zbl0096.08602MR23 #A3362
  12. [12] E. MAZET, Une majoration de λ1 du type de Cheeger (C. R. Acad. Sc., t. 277, série A, 1973). Zbl0264.53021MR50 #14581
  13. [13] H. P. MCKEAN, An Upper Bound to the Spectrum on a Manifold of Negative Curvature (J. of Diff. Geom., Vol. 4, 1970, p. 359-366). Zbl0197.18003MR42 #1009
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  15. [15] F. WARNER, Extensions of the Rauch Comparison Theorem to Submanifolds (Trans. Amer. Math. Soc., Vol. 122, 1966, p. 341-356). Zbl0139.15601MR34 #759
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Citations in EuDML Documents

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  1. Christopher B. Croke, Some isoperimetric inequalities and eigenvalue estimates
  2. Peter Li, On the Sobolev constant and the p -spectrum of a compact riemannian manifold
  3. Paul C. Yang, Shing-Tung Yau, Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds
  4. Olli Martio, V. Miklyukov, M. Vuorinen, Estimates for the energy integral of quasiregular mappings on Riemannian manifolds and isoperimetry
  5. Sylvestre Gallot, Minorations sur le λ 1 des variétés riemanniennes
  6. Emmanuel Hebey, Meilleures constantes et inégalités de Sobolev optimales sur les variétés riemanniennes compactes
  7. Peter Buser, A note on the isoperimetric constant
  8. Andrea Cianchi, Eigenfunctions of the Laplace-Beltrami Operator, and Isoperimetric and Isocapacitary Inequalities

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