论文标题
关于无限体积的几何有限双曲线歧管的特征值
On Eigenvalues of Geometrically Finite Hyperbolic Manifolds with Infinite Volume
论文作者
论文摘要
让$ m $成为无限体积的定向几何双曲线歧管，尺寸至少$ 3 $。对于所有$ k \ geq 0 $，我们在$ m $ $ m $ $ k $ th的特征值上提供了$ m $ $ m $的$ k $ th，$ k $ th the the the the the the eigenvalue the convex Core的某些社区的特征值，最高为常数。 As an application, we recover a theorem similar to the one of Burger and Canary which bounds the bottom $λ_0$ of the spectrum from below by $\frac{c}{\text{vol}(C_1(M))^2}$, where $C_1(M)$ is the $1$-neighborhood of the convex core and $c$ is a constant.
Let $M$ be an oriented geometrically finite hyperbolic manifold of infinite volume with dimension at least $3$. For all $k \geq 0$, we provide a lower bound on the $k$th eigenvalue of the Laplace-Beltrami operator of $M$ by the $k$th eigenvalue of some neighborhood of the thick part of the convex core, up to a constant. As an application, we recover a theorem similar to the one of Burger and Canary which bounds the bottom $λ_0$ of the spectrum from below by $\frac{c}{\text{vol}(C_1(M))^2}$, where $C_1(M)$ is the $1$-neighborhood of the convex core and $c$ is a constant.
