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The first eigenvalue of the Laplacian on two dimensional Riemannian manifolds. (English) Zbl 0486.53035

MSC:
53C20 Global Riemannian geometry, including pinching
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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[1] M. BERGER, P. GAUDHON AND E. MAZET, Le spectre d’une variete riemannienne, Lecture Notes in Math. 194, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
[2] P. BUSER, On Cheeger’s inequality I ^/z, 2/4, Proceedings of Symposia in Pure Math Vol. 36, American Math. Soc. Providence, Rhode Island, 1980, 29-77. · Zbl 0432.58024
[3] I. CHAVEL AND E. A. FELDMAN, Spectra of domains in compact manifolds, J. Functiona Analysis 30 (1978), 198-222. · Zbl 0392.58016 · doi:10.1016/0022-1236(78)90070-8
[4] J. CHEEGER, A Lower Bound for the Smallest Eigenvalue of the Laplacian, Problems i Analysis, Princeton Univ. Press, Princeton, N. J., 1970. · Zbl 0212.44903
[5] T. MATSUZAWA AND S. TANNO, Estimates of the first eigenvalues of a big cup domai of a 2-sphere, (preprint). · Zbl 0498.53033 · numdam:CM_1982__47_1_95_0 · eudml:89561
[6] M. SCHIFFER AND D. C. SPENCER, Functionals of Finite Riemann Surfaces, Princeto Univ. Press, Princeton, N. J., 1954. · Zbl 0059.06901
[7] S. OZAWA, Singular variation of domains and eigenvalues of the Laplacian, · Zbl 0483.35064 · doi:10.1215/S0012-7094-81-04842-0
[8] S. OZAWA, Surgery of domains and Green’s kernels of the Laplacian, Proc. Japan Acad 56 (1980), 459-461. · Zbl 0468.35033 · doi:10.3792/pjaa.56.459
[9] S. OZAWA, Singular Hadamard’s variation of domains and eigenvalues of the Laplacian, II, Ibid. 57 (1981), 242-246. · Zbl 0509.35060 · doi:10.3792/pjaa.57.242
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