Some isoperimetric inequalities and eigenvalue estimates
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 13 (1980) no. 4, pp. 419-435.
@article{ASENS_1980_4_13_4_419_0,
     author = {Croke, Christopher B.},
     title = {Some isoperimetric inequalities and eigenvalue estimates},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {419--435},
     publisher = {Elsevier},
     volume = {Ser. 4, 13},
     number = {4},
     year = {1980},
     doi = {10.24033/asens.1390},
     mrnumber = {83d:58068},
     zbl = {0465.53032},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1390/}
}
TY  - JOUR
AU  - Croke, Christopher B.
TI  - Some isoperimetric inequalities and eigenvalue estimates
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1980
SP  - 419
EP  - 435
VL  - 13
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.24033/asens.1390/
DO  - 10.24033/asens.1390
LA  - en
ID  - ASENS_1980_4_13_4_419_0
ER  - 
%0 Journal Article
%A Croke, Christopher B.
%T Some isoperimetric inequalities and eigenvalue estimates
%J Annales scientifiques de l'École Normale Supérieure
%D 1980
%P 419-435
%V 13
%N 4
%I Elsevier
%U http://archive.numdam.org/articles/10.24033/asens.1390/
%R 10.24033/asens.1390
%G en
%F ASENS_1980_4_13_4_419_0
Croke, Christopher B. Some isoperimetric inequalities and eigenvalue estimates. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 13 (1980) no. 4, pp. 419-435. doi : 10.24033/asens.1390. http://archive.numdam.org/articles/10.24033/asens.1390/

[1] M. Berger, Lectures on Geodesics in Riemannian Geometry, Tata Institute, Bombay, 1965. | MR | Zbl

[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. | MR | Zbl

[3] M. Berger, Une inégalité universelle pour la première valeur propre du laplacien (Bull. Soc. math. Fr., T. 107, 1979, pp. 3-9). | Numdam | MR | Zbl

[4] A. Besse, Manifolds All of Whose Geodesics are Closed (Ergebnisse der Mathematik, Vol. 93, Springer, Berlin-Heidelberg-New York, 1978). | MR | Zbl

[5] R. Bishop and R. Crittenden, Geometry of Manifolds, Academic Press, 1964. | 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, Princeton, 1970, pp. 195-199). | MR | Zbl

[7] J. Cheeger and D. G. Ebin, Comparison Theorems in Riemannian Geometry, North Holland, Amsterdam, 1975. | MR | Zbl

[8] S.-Y. Cheng, On the Hayman-Osserman-Taylor Inequality (preprint).

[9] L. W. Green, Auf Wiedersehenflächen (Ann. of Math., Vol. 78, 1963, pp. 289-299). | MR | Zbl

[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). | Numdam | MR | Zbl

[11] R. Osserman, The Isoperimetric Inequality (Bull. Amer. Math. Soc., Vol. 87, 1978, pp. 1182-1238). | MR | Zbl

[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. | MR | Zbl

[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]. | Numdam | MR | Zbl

Cité par Sources :