论文标题
具有多个边界组件的表面低螺旋藻特征值的估计值
Estimates for low Steklov eigenvalues of surfaces with several boundary components
论文作者
论文摘要
在本文中，我们为第一个非零的steklov特征值$σ_1$提供了可计算的下限。这些估计表明，$ m $远离边界的几何形状如何影响该特征值。它们涉及特定于具有边界的歧管（例如边界外直径）的几何量。在第二部分中，我们给出了屈曲表面的低骨特征值的较低和上部估计，就某些大地测量家族的长度而言，具有地理边界。该结果类似于Schoen，Wolpert和Yau在封闭的双曲表面上用于拉普拉斯特征值的众所周知的结果。
In this article, we give computable lower bounds for the first non-zero Steklov eigenvalue $σ_1$ of a compact connected 2-dimensional Riemannian manifold $M$ with several cylindrical boundary components. These estimates show how the geometry of $M$ away from the boundary affects this eigenvalue. They involve geometric quantities specific to manifolds with boundary such as the extrinsic diameter of the boundary. In a second part, we give lower and upper estimates for the low Steklov eigenvalues of a hyperbolic surface with a geodesic boundary in terms of the length of some families of geodesics. This result is similar to a well known result of Schoen, Wolpert and Yau for Laplace eigenvalues on a closed hyperbolic surface.
