A note on the isoperimetric constant

 Access to full text

 Full (PDF)

1. [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). Zbl0327.49043MR54 #8420
2. [2] M. BERGER, Une inégalité universelle pour la première valeur propre du laplacien (Bull. Soc. Math. Fr., Vol. 107, 1979, pp. 3-9). Zbl0399.35080MR80f:58046
3. [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). Zbl0421.53028MR82b:53047
4. [4] L. BISHOP and R. CRITTENDEN, Geometry of Manifolds, Academic Press, New York, London, 1964. Zbl0132.16003
5. [5] R. BROOKS, Amenability and the Spectrum of the Laplacian, Maryland, April 1981 (Preprint). Zbl0495.58029
6. [6] P. BUSER, Ueber den ersten Eigenwert des Laplace-Operators auf kompakten Flächen (Comment. Math. Helv., Vol. 54, 1979, pp. 477-493). Zbl0433.58020MR81g:58038
7. [7] P. BUSER, Beispiele für λ1 auf kompakten Mannigfaltigkeiten Math. Z., Vol. 165, 1977, pp. 107-133. Zbl0377.35058MR80d:58070
8. [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). Zbl0432.58024MR83b:58075
9. [9] I. CHAVEL, A Note on Manifolds with Thin Handles (Preprint). 
10. [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). Zbl0212.44903MR53 #6645
11. [11] B. CROKE, Some Isoperimetric Inequalities and Eigenvalue Estimates (Ann. Scient. Éc. Norm. Sup. 4e série, T. 13, 1980, pp. 419-435). Zbl0465.53032MR83d:58068
12. [12] H. DONNELLY, On the Essential Spectrum of a Complete Riemannian Manifold (Topology, Vol. 20, 1980, pp. 1-14). Zbl0463.53027MR81j:58081
13. [13] H. FEDERER, Geometric Measure Theory, Springer Verlag, New York, etc., 1969. Zbl0176.00801MR41 #1976
14. [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). Zbl0194.35803MR41 #5601
15. [15] M. GAGE, Upper Bounds for the First Eigenvalue of the Laplace-Beltrami Operator (Indiana Univ. Math. J., Vol. 29, 1980, pp. 897-912. Zbl0465.53031MR82b:58095
16. [16] M. GROMOV, Paul Levy's Isoperimetric Inequality (Preprint). 
17. [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). Zbl0416.53027MR80i:53026
18. [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). Zbl0466.53023MR82h:58054
19. [19] U. MASSARI, Esistenza e Regolarità delle Ipersuperfici di Curvatura Media Assegnata in ℝn (Arch. Rat. Mech. Anal., Vol. 55, 1974, pp. 357-382). Zbl0305.49047MR50 #8240
20. [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). Zbl0041.42701MR11,108b
21. [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). Zbl0374.52008MR56 #17297
22. [22] R. OSSERMAN, The Isoperimetric Inequality (Bull. Amer. Math. Soc., Vol. 84, 1978, pp. 1182-1238). Zbl0411.52006MR58 #18161
23. [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). Zbl0446.58018MR81i:58052
24. [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). Zbl0325.53039MR53 #1478

1. Gilles Courtois, La première valeur propre non nulle du laplacien des $p-$formes
2. Carlos Matheus, Gabriela Weitze-Schmithüsen, Explicit Teichmüller curves with complementary series
3. Hacene Djellout, Liming Wu, Lipschitzian norm estimate of one-dimensional Poisson equations and applications
4. Alexander Grigor'yan, Laurent Saloff-Coste, Stability results for Harnack inequalities
5. Bruno Colbois, Le spectre du laplacien agissant sur les $p-$formes différentielles
6. Michel Ledoux, Inégalités isopérimétriques en analyse et probabilités
7. Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Trace inequalities for Carnot-Carathéodory spaces and applications