no. 1
On a lower bound for the first eigenvalue of the Laplace operator on a riemannian manifold
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 17 (1984) no. 1, pp. 31-44 
@article{ASENS_1984_4_17_1_31_0,
     author = {Kasue, Atsushi},
     title = {On a lower bound for the first eigenvalue of the {Laplace} operator on a riemannian manifold},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {31--44},
     year = {1984},
     publisher = {Elsevier},
     volume = {Ser. 4, 17},
     number = {1},
     doi = {10.24033/asens.1464},
     mrnumber = {85i:58120},
     zbl = {0553.53026},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/asens.1464/}
}
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Kasue, Atsushi. On a lower bound for the first eigenvalue of the Laplace operator on a riemannian manifold. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 17 (1984) no. 1, pp. 31-44. doi: 10.24033/asens.1464

[1] J. Barta, Sur la vibration fondamentale d'une membrane (Comptes Rendus de l'Acad. des Sci., Paris, Vol. 204, 1937, pp. 472-473). | JFM

[2] P. Bérard et D. Meyer, Inégalités isopérimétriques et applications (Ann. scient. Éc. Norm. Sup., Paris, 4e série, t. 15, 1982, pp. 513-542). | Zbl | MR | Numdam

[3] R. L. Bishop and B. O'Neill, Manifolds of negative curvature (Trans. Amer. Math. Soc., Vol. 145, 1969, pp. 1-49). | Zbl | MR

[4] J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative curvature (J. Differential Geometry, Vol. 6, 1971, pp. 119-128). | Zbl | MR

[5] R. Courant and D. Hilbert, Methods of Mathematical Physics, Interscience Pub., Inc., New York, 1970.

[6] P. Eberlein and B. O'Neill, Visibility manifolds (Pacific J. Math., Vol. 46, 1973, pp. 45-109). | Zbl | MR

[7] S. Friedland and W. K. Hayman, Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions (Comm. Math. Helvetici, Vol. 51, 1976, pp. 133-161). | Zbl | MR

[8] S. Gallot, Minorations sur le λ1 des variétés riemanniennes, Séminaire Bourbaki 33e année, 1980-1981, n° 569. | Zbl | Numdam

[9] S. Gallot, A Sobolev inequality and some geometric applications, preprint (séminaire Franco-Japonais de Kyoto).

[10] R. E. Greene and H. Wu, On the subharmonicity and plurisubharmonicity of geodesically convex function, (Indiana Univ., Math. J., Vol. 22, 1973, pp. 641-653). | Zbl | MR

[11] R. E. Greene and H. Wu, D∞ approximations of convex, subharmonic and plurisubharmonic functions (Ann. scient. Éc. Norm. Sup., 4e série, t. 12. 1979, pp. 47-84). | Zbl | MR | Numdam

[12] M. Gromov, Paul Levy's isoperimetric inequalities, Publications I.H.E.S., 1981.

[13] E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds (Ann. scient. Éc. Norm. Sup., Paris, Vol. 11, 1978, pp. 451-470). | Zbl | MR | Numdam

[14] A. Kasue, On a Riemannian manifold with a pole (Osaka J. Math., Vol. 18, 1981, pp. 109-113). | Zbl | MR

[15] A. Kasue, A Laplacian comparison theorem and function theoretic properties of a complete Riemannian manifold (Japan J. Math., Vol. 18, 1982, pp. 309-341). | Zbl | MR

[16] A. Kasue, Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary (J. Math. Soc. Japan, Vol. 35, 1983, pp. 117-131). | Zbl | MR

[17] M. G. Krein, On certain problems of the maximum and minimum of characteristic values and on the Lyapunov zones of stability (A.M.S. Trans., Vol. 2, n° 1, 1955, pp. 163-187). | Zbl | MR

[18] A. Lichnerowicz, Géométrie des groupes de transformations, Dunod, 1958. | Zbl | MR

[19] P. Li and S. T. Yau, Estimates of eigenvalues of a compact Riemannian manifold (Proc. Symp. Pure Math. A.M.S., Vol. 36, 1980, pp. 205-239). | Zbl | MR

[20] H. P. Mckean, An upper bound to the spectrum on a manifold of negative curvature (J. Differential Geometry, Vol. 4, 1970, pp. 359-366). | Zbl | MR

[21] M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere (J. Math. Soc. Japan, Vol. 14, 1962, pp. 333-340). | Zbl | MR

[22] W. A. Poor Jr., Some results on nonnegatively curved manifolds (J. Differential Geometry, Vol. 9, 1974, pp. 583-600). | Zbl | MR

[23] R. C. Reilly, Applications of the Hessian operator in a Riemannian manifold, (Indiana Univ. Math. J., Vol. 26, 1977, pp. 459-472). | Zbl | MR

[24] H. Wu, An elementary method in the study of nonnegative curvature (Acta. Math., Vol. 142, 1979, pp. 57-78). | Zbl | MR

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