论文标题
大属的退化双曲表面和光谱间隙
Degenerating hyperbolic surfaces and spectral gaps for large genus
论文作者
论文摘要
在本文中，我们研究了两个连续的特征值$λ_{i}-λ_{i-1} $最高$ i = 2g-2 $ for laplacian在属$ g $属的双曲表面上的差异，并表明在moduli空间上的频谱上的差距是$ \ frac的无限;还建立了在退化双曲线表面上特征值的最低特征原理。
In this article we study the differences of two consecutive eigenvalues $λ_{i}-λ_{i-1}$ 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.
