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Petites valeurs propres du laplacien sur une surface de Riemann compacte et graphes. (Small eigenvalues of the Laplacian on a compact Riemann surface and graphs). (French) Zbl 0582.53034

In the special case of a compact Riemann surface with curvature -1, our result sharpens Schoen-Wolpert-Yau’s theorem [R. Schoen, S. Wolpert and S. T. Yau, Geometry of the Laplace operator, Honolulu/Hawaii 1979, Proc. Symp. Pure Math. 36, 279-285 (1980; Zbl 0446.58018)] for eigenvalues approaching 0.

MSC:

53C20 Global Riemannian geometry, including pinching
58J50 Spectral problems; spectral geometry; scattering theory on manifolds

Citations:

Zbl 0446.58018
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