ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract LetM be a complete Riemannian surface with constant curvature −1, infinite volume, and a finitely generated fundamental group. Denote by λ(M) the lowest eigenvalue of the Laplacian onM, and let Φ M be the associated eigenfunction. We estimate the size of λ(M) and the shape of Φ M by a finite procedure which has an electrical circuit analogue. Using the Margulis lemma, we decomposeM into its thick and thin parts. On the compact thick components, we show that Φ M varies from a constant value by no more thanO( $$\sqrt {\lambda (M)}$$ ). The estimate for λ(M) is calculable in terms of the topology ofM and the lengths of short geodesics ofM. An analogous theorem of the compact case was treated in [SWY].
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01211062
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