no. 4
Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 8 (1975) no. 4, pp. 487-507. 
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     author = {Yau, Shing-Tung},
     title = {Isoperimetric constants and the first eigenvalue of a compact riemannian manifold},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {487--507},
     publisher = {Elsevier},
     volume = {Ser. 4, 8},
     number = {4},
     year = {1975},
     doi = {10.24033/asens.1299},
     mrnumber = {53 #1478},
     zbl = {0325.53039},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1299/}
}
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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, Série 4, Tome 8 (1975) no. 4, pp. 487-507. doi : 10.24033/asens.1299. http://archive.numdam.org/articles/10.24033/asens.1299/

[1] M. Berger, P. Gauduchon, et E. Mazet, Le spectre d'une variété riemannienne (Lecture Notes in Math., N°. 194, Springer). | MR | Zbl

[2] R. Bishop and R. Cristtenden, Geometry of Manifolds, Academic Press, 1964. | Zbl

[3] J. D. Burago and V. A. Zalgaller, Isoperimetric Problems for Regions on a Surface Having Restricted Width (Proceedings of Stek. Inst. Math., N°. 76, 1965.) | MR | Zbl

[4] I. Chavel and E. Feldman, The First Eigenvalue of the Laplacian on Manifolds of Non-Negative Curvature (to appear).

[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). | MR | Zbl

[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. | Zbl

[7] S. Y. Cheng, Eigenfunctions and Eigenvalues of Laplacian (to ppear in the Proceedings of Symposium on Differential Geometry). | Zbl

[8] S. Y. Cheng, Eigenvalue Comparison Theorems and its Geometric Applications (Math. Z., Vol. 143, 1975, p. 289-297.) | MR | Zbl

[9] L. Keen, Collars on Riemann Surfaces, In “Discontinuous Groups and Riemann Surfaces”, edited by by GREENBERG, Princeton University Press, 1974, p. 263-268. | MR | Zbl

[10] A. Huber, On the Isoperimetric Inequality on Surfaces of Variable Gaussian Curvature (Ann. of Math., Vol. 60, 1954, p. 237-247). | MR | Zbl

[11] J. Hersch, Caractérisation variationnelle d'une somme de valeurs propres consécutives (C. R. Acad. Sc., t. 252, 1961, série A, p. 1714-1716). | MR | Zbl

[12] E. Mazet, Une majoration de λ1 du type de Cheeger (C. R. Acad. Sc., t. 277, série A, 1973). | MR | Zbl

[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). | MR | Zbl

[14] H. Federer, Geometric Measure Theory, Springer, 1969. | MR | Zbl

[15] F. Warner, Extensions of the Rauch Comparison Theorem to Submanifolds (Trans. Amer. Math. Soc., Vol. 122, 1966, p. 341-356). | MR | Zbl

[16] D. Hoffman, and J. Spruck, Sobolev and Isoperimetric Inequalities for Riemannian Submanifolds (to appear). | Zbl

[17] J. Michael, and L. Simon, Sobolev and Mean Value Inequalities on Generalized Submanifolds of Rn (Comm. Pure and Appl. Math., 1973, p. 361-379). | MR | Zbl

[18] L. Green, A Theorem of E. Hopf (Mich. Math. J., Vol., 5, 1958, p. 31-34). | MR | Zbl

[19] J. Cheeger, and D. Gromoll, The Splitting Theorem for Manifolds of Non-Negative Ricci Curvature (J. Diff. Geom., Vol. 6, 1971, p. 119-128). | MR | Zbl

[20] J. Milnor, A Note on Curvature and Fundamental Group (J. Diff. Geom., Vol. 2, 1968, p. 1-8). | MR | Zbl

[21] H. S. Ruse, A. G. Walker, and T. J. Willmore, Harmonic Spaces, Edizioni Cremonese, Roma. | Zbl

[22] A. C. Allamigeon, Propriétés globales des espaces riemanniens harmoniques (Ann. Inst. Fourier, Vol. 15, N°. 2, 1965, p. 91-132). | Numdam | MR | Zbl

[23] C. B. Morrey, Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York, 1966. | MR | Zbl

[24] W. Klingberg, Contributions to Riemannian Geometry in the Large (Ann. Math., Vol. 69, 1959, p. 654-666). | MR | Zbl

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