A note on the isoperimetric constant
Buser, Peter
Annales scientifiques de l'École Normale Supérieure, Tome 15 (1982), p. 213-230 / Harvested from Numdam
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@article{ASENS_1982_4_15_2_213_0,
     author = {Buser, Peter},
     title = {A note on the isoperimetric constant},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {15},
     year = {1982},
     pages = {213-230},
     doi = {10.24033/asens.1426},
     mrnumber = {84e:58076},
     zbl = {0501.53030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1982_4_15_2_213_0}
}

Buser, Peter. A note on the isoperimetric constant. Annales scientifiques de l'École Normale Supérieure, Tome 15 (1982) pp. 213-230. doi : 10.24033/asens.1426. http://gdmltest.u-ga.fr/item/ASENS_1982_4_15_2_213_0/

[1] F. Almgren, Existence and Regularity Almost Everywhere of Solutions to Elliptic Variational Problems with Constraints (Mem. Amer. Math. Soc., Vol. 4, No. 165, 1976). | MR 54 #8420 | Zbl 0327.49043

[2] M. Berger, Une inégalité universelle pour la première valeur propre du laplacien (Bull. Soc. Math. Fr., Vol. 107, 1979, pp. 3-9). | Numdam | MR 80f:58046 | Zbl 0399.35080

[3] M. Berger, Une borne inférieure pour le volume d'une variété riemannienne en fonction du rayon d'injectivité (Ann. Inst. Fourier, Grenoble, Vol. 30, 1980, pp. 259-265). | Numdam | MR 82b:53047 | Zbl 0421.53028

[4] L. Bishop and R. Crittenden, Geometry of Manifolds, Academic Press, New York, London, 1964. | Zbl 0132.16003

[5] R. Brooks, Amenability and the Spectrum of the Laplacian, Maryland, April 1981 (Preprint).

[6] P. Buser, Ueber den ersten Eigenwert des Laplace-Operators auf kompakten Flächen (Comment. Math. Helv., Vol. 54, 1979, pp. 477-493). | MR 81g:58038 | Zbl 0433.58020

[7] P. Buser, Beispiele für λ1 auf kompakten Mannigfaltigkeiten Math. Z., Vol. 165, 1977, pp. 107-133. | MR 80d:58070 | Zbl 0377.35058

[8] P. Buser, On Cheeger's Inequality λ1 ≧ h²/4, in Geometry of the Laplace Operator (Proceedings of Symposia in Pure Mathematics, Vol. 36, 1980 pp. 29-77). | MR 83b:58075 | Zbl 0432.58024

[9] I. Chavel, A Note on Manifolds with Thin Handles (Preprint).

[10] 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, pp. 195-199). | MR 53 #6645 | Zbl 0212.44903

[11] B. Croke, Some Isoperimetric Inequalities and Eigenvalue Estimates (Ann. Scient. Éc. Norm. Sup. 4e série, T. 13, 1980, pp. 419-435). | Numdam | MR 83d:58068 | Zbl 0465.53032

[12] H. Donnelly, On the Essential Spectrum of a Complete Riemannian Manifold (Topology, Vol. 20, 1980, pp. 1-14). | MR 81j:58081 | Zbl 0463.53027

[13] H. Federer, Geometric Measure Theory, Springer Verlag, New York, etc., 1969. | MR 41 #1976 | Zbl 0176.00801

[14] H. Federer, The Singular Sets of Area Minimizing Rectifiable Currents with Codimension One and of Area Minimizing Flat Chains Modulo two with Arbitrary Codimension (Bull. Amer. Math. Soc., Vol. 76, 1970, pp. 767-771). | MR 41 #5601 | Zbl 0194.35803

[15] M. Gage, Upper Bounds for the First Eigenvalue of the Laplace-Beltrami Operator (Indiana Univ. Math. J., Vol. 29, 1980, pp. 897-912. | MR 82b:58095 | Zbl 0465.53031

[16] M. Gromov, Paul Levy's Isoperimetric Inequality (Preprint).

[17] E. Heintze and H. Karcher, A General Comparison Theorem with Applications to Volume Estimates for Submanifolds (Ann. Scient. Éc. Norm. Sup., 4e série, T. 11, 1978, pp. 451-470). | Numdam | MR 80i:53026 | Zbl 0416.53027

[18] P. Li, On the Sobolev Constant and the p-Spectrum of a Compact Riemannian Manifold (Ann. Scient. Ec. Norm. Sup., 4e série, T. 13, 1980, pp. 451-467). | Numdam | MR 82h:58054 | Zbl 0466.53023

[19] U. Massari, Esistenza e Regolarità delle Ipersuperfici di Curvatura Media Assegnata in ℝn (Arch. Rat. Mech. Anal., Vol. 55, 1974, pp. 357-382). | MR 50 #8240 | Zbl 0305.49047

[20] S. Minakshisundaram and Å. Plejel, Some Properties of the Eigenfunctions of the Laplace-Operator on Riemannian Manifolds (Canad. J. Math., Vol. 1, 1949, pp. 242-256). | MR 11,108b | Zbl 0041.42701

[21] R. Osserman, A Note on Hayman's Theorem on the Bass Note of a Drum (Comment. Math. Helv. Vol. 52, 1977, pp. 545-555). | MR 56 #17297 | Zbl 0374.52008

[22] R. Osserman, The Isoperimetric Inequality (Bull. Amer. Math. Soc., Vol. 84, 1978, pp. 1182-1238). | MR 58 #18161 | Zbl 0411.52006

[23] R. Schoen, S. Wolpert and S. T. Yau, Geometric Bounds on the Low Eigenvalues of a Compact Surface, in Geometry of the Laplace Operator (Proceedings of Symposia in Pure Mathematics, Vol. 36, 1980, pp. 279-285). | MR 81i:58052 | Zbl 0446.58018

[24] S. T. Yau, Isoperimetric Constants and the First Eigenvalue of a Compact Riemannian Manifold (Ann. Scient. Éc. Norm. Sup., 4e série, T. 8, 1975, pp. 487-507). | Numdam | MR 53 #1478 | Zbl 0325.53039