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arXiv · 1406.1080

On largeness and multiplicity of the first eigenvalue of hyperbolic surfaces

Sugata Mondal
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Abstract

We apply topological methods to study the smallest non-zero number $λ_1$ in the spectrum of the Laplacian on finite area hyperbolic surfaces. For closed hyperbolic surfaces of genus two we show that the set $\{S \in {\mathcal{M}_2}: {λ_1}(S) > 1/4 \}$ is unbounded and disconnects the moduli space ${\mathcal{M}_2}$.

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Sugata Mondal. 2014-10-08. On largeness and multiplicity of the first eigenvalue of hyperbolic surfaces. https://doi.org/10.1007/s00209-015-1486-8

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