Geodesic
On the spectra of hyperbolic surfaces without thin handles
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 60-66 
M. B. Dubashinskiy. On the spectra of hyperbolic surfaces without thin handles. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 60-66. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a5/
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     author = {M. B. Dubashinskiy},
     title = {On the spectra of hyperbolic surfaces without thin handles},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--66},
     year = {2018},
     volume = {467},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We obtain a sharp lower estimate on eigenvalues of Laplace–Beltrami operator on a hyperbolic surface with injectivity radius bounded from the below.

[1] P. Buser, Geometry and Spectra of Compact Riemann Surfaces Birkhäuser, 2010, reprint izdaniya 1992 g. | MR

[2] P. Buser, “Cubic graphs and the first eigenvalue of a Riemann surface”, Math. Z., 162 (1978), 87–99 | DOI | MR | Zbl

[3] J.-P. Otal, E. Rosas, “Pour toute surface hyperbolique de genre $g$, $\lambda_{2g-2}>1/4$”, Duke Math. J., 150:1 (2009), 101–115 | DOI | MR | Zbl

[4] J. Cheeger, “A lower bound for the smallest eigenvalue of the Laplacian”, Problems in analysis, A symposium in honor of S. Bochner, Princeton Univ. Press, Princeton, NJ, 1970, 195–199 | MR | Zbl

[5] S.-T. Yau, “Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold”, Ann. Sci. Ecole Norm. Sup., 8:4 (1975), 487–507 | DOI | MR | Zbl