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In this article we study the differences of two consecutive eigenvalues$\lambda_{i}-\lambda_{i-1}$ up to $i=2g-2$ for the Laplacian on hyperbolicsurfaces of genus $g$, and show that the supremum of such spectral gaps overthe moduli space has infimum limit at least $\frac{1}{4}$ as genus goes toinfinity. A min-max principle for eigenvalues on degenerating hyperbolicsurfaces is also established.

Degenerating hyperbolic surfaces and spectral gaps for large genus