Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 7 (1980) no. 1, pp. 55-63.
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     title = {Eigenvalues of the laplacian of compact {Riemann} surfaces and minimal submanifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Yang, Paul C.; Yau, Shing-Tung. Eigenvalues of the laplacian of compact Riemann surfaces and minimal submanifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 7 (1980) no. 1, pp. 55-63. http://www.numdam.org/item/ASNSP_1980_4_7_1_55_0/

[1] M. Berger, Sur les premières valeurs propres des variétés Riemanniennes, Compositio Math., 26 (1973), pp. 129-149. | Numdam | MR | Zbl

[2] S.-Y. Cheng, Eigenvalues comparison theorems and its geometric applications, Math. Z., 143 (1975), pp. 289-297. | MR | Zbl

[3] J. Hersch, Quatre properiétés isopérimétriques de membranes sphériques homogènes, C. R. Acad. Sci. Paris, 270 (1970), pp. 1645-1648. | MR | Zbl

[4] S. Kobayashi - K. Nomizu, Foundations of Differential Geometry, Volume II. | Zbl

[5] L.E. Payne - G. Polya - H.F. Weinberger, On the ratio of consecutive eigenvalues, J. Mathematical Phys., 35 (1956), pp. 289-298. | MR | Zbl

[6] S. Tanno, The first eigenvalues of the laplacian on spheres, to appear in Tôhoku Math. J. | MR | Zbl

[7] H. Urakawa: On the least positive eigenvalue of the laplacian for riemannian manifolds II, preprint. | MR

[8] S.-T. Yau, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Sci. École Norm. Sup., 8 (1975), pp. 487-507. | Numdam | MR | Zbl