Some isoperimetric inequalities and eigenvalue estimates

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1. [1] M. BERGER, Lectures on Geodesics in Riemannian Geometry, Tata Institute, Bombay, 1965. Zbl0165.55601MR35 #6100
2. [2] M. BERGER, Some Relations Between Volume, Injectivity Radius, and Convexity Radius in Riemannian Manifolds, Differential Geometry and Relativity, D. Reidel Publishing Co., Dordrecht-Boston, 1976, pp. 33-42. Zbl0342.53038MR56 #6562
3. [3] M. BERGER, Une inégalité universelle pour la première valeur propre du laplacien (Bull. Soc. math. Fr., T. 107, 1979, pp. 3-9). Zbl0399.35080MR80f:58046
4. [4] A. BESSE, Manifolds All of Whose Geodesics are Closed (Ergebnisse der Mathematik, Vol. 93, Springer, Berlin-Heidelberg-New York, 1978). Zbl0387.53010MR80c:53044
5. [5] R. BISHOP and R. CRITTENDEN, Geometry of Manifolds, Academic Press, 1964. Zbl0132.16003MR29 #6401
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, Princeton, 1970, pp. 195-199). Zbl0212.44903MR53 #6645
7. [7] J. CHEEGER and D. G. EBIN, Comparison Theorems in Riemannian Geometry, North Holland, Amsterdam, 1975. Zbl0309.53035MR56 #16538
8. [8] S.-Y. CHENG, On the Hayman-Osserman-Taylor Inequality (preprint). 
9. [9] L. W. GREEN, Auf Wiedersehenflächen (Ann. of Math., Vol. 78, 1963, pp. 289-299). Zbl0116.13503MR27 #5206
10. [10] P. LI, On the Sobolev Constant and the p-Spectrum of a Compact Riemannian Manifold (Ann. scient. Éc. Norm. Sup., T. 13, 1980, pp. 451-467). Zbl0466.53023MR82h:58054
11. [11] R. OSSERMAN, The Isoperimetric Inequality (Bull. Amer. Math. Soc., Vol. 87, 1978, pp. 1182-1238). Zbl0411.52006MR58 #18161
12. [12] L. A. SANTALÓ, Integral Geometry and Geometric Probability (Encyclopedia of Mathematics and Its Applications), Addison-Wesley, London-Amsterdam-Dom Mills, Ontario-Sydney-Tokyo, 1976. Zbl0342.53049MR55 #6340
13. [13] S.-T. YAU, Isoperimetric Constants and the First Eigenvalue of a Compact Riemannian Manifold [Ann. scient. Éc. Norm. Sup., (4), T. 8, 1975, pp. 487-507]. Zbl0325.53039MR53 #1478

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