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 hyperbolic surfaces of genus $g$, and show that the supremum of such spectral gaps over the moduli space has infimum limit at least $\frac{ 1}{ 4}$ as genus goes to infinity. A min-max principle for eigenvalues on degenerating hyperbolic surfaces is also established.
Categories: math.DG math.AP