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Ground state and lowest eigenvalue of the Laplacian for non-compact hyperbolic surfaces. (English) Zbl 0602.58046

Let M be a complete Riemannian surface with constant curvature -1 and a finitely generated fundamental group. The authors estimate the first eigenvalue of the Laplacian giving upper and lower bounds, and they give information on the shape of the basic eigenfunction.
Reviewer: U.Simon

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C20 Global Riemannian geometry, including pinching
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References:

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