On largeness and multiplicity of the first eigenvalue of finite area hyperbolic surfaces
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چکیده
We apply topological methods to study the smallest non-zero number λ1 in the spectrum of the Laplacian on finite area hyperbolic surfaces. For closed hyperbolic surfaces of genus two we show that the set {S ∈ M2 : λ1(S) > 1 4 } is unbounded and disconnects the moduli spaceM2. Using this, for genus g ≥ 3, we show the existence of eigenbranches that start as λ1 and eventually becomes > 1 4 .
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تاریخ انتشار 2015