Estimates of the first eigenvalue of a big cup domain of a 2-sphere
Compositio Mathematica, Tome 47 (1982) no. 1, p. 95-100
@article{CM_1982__47_1_95_0,
     author = {Matsuzawa, Tadayuki and Tanno, Shukichi},
     title = {Estimates of the first eigenvalue of a big cup domain of a 2-sphere},
     journal = {Compositio Mathematica},
     publisher = {Martinus Nijhoff Publishers},
     volume = {47},
     number = {1},
     year = {1982},
     pages = {95-100},
     zbl = {0498.53033},
     mrnumber = {668783},
     language = {en},
     url = {http://www.numdam.org/item/CM_1982__47_1_95_0}
}
Matsuzawa, Tadayuki; Tanno, Shukichi. Estimates of the first eigenvalue of a big cup domain of a 2-sphere. Compositio Mathematica, Tome 47 (1982) no. 1, pp. 95-100. http://www.numdam.org/item/CM_1982__47_1_95_0/

[1] J.L. Barbosa and M. Do Carmo: Stability of minimal surfaces and eigenvalues of the Laplacian. Math. Zeit. 173 (1980) 13-28. | MR 584346 | Zbl 0417.53033

[2] I. Chavel and E.A. Feldman: Spectra of domains in compact manifolds. Journ. Funct. Anal. 30 (1978) 198-222. | MR 515225 | Zbl 0392.58016

[3] A. Debiard, B. Gaveau et E. Mazet: Temps de sortie des boules normales et minoration local de λ1. Compt. Rend. Acad. Sci. Paris 278 (1974) 795-798. | Zbl 0274.53039

[4] S. Friedland and W.K. Hayman: Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions. Comm. Math. Helv. 51 (1976) 133-161. | MR 412442 | Zbl 0339.31003

[5] S. Ozawa: The first eigenvalue of the Laplacian of two-dimensional Reimannian manifold (preprint; Department of Mathematics, Tokyo University, Japan). | MR 651702