论文标题
球形对称歧管上的特征值
Eigenvalues on Spherically Symmetric Manifolds
论文作者
论文摘要
在本文中，我们将探索球形对称歧管上的球上的dirichlet laplace特征值。我们将将任何Dirichlet Laplace特征值与相同半径相同的欧几里得空间中的球上的相应的Dirichlet Laplace特征值进行比较。作为一种特殊情况，我们将证明球上的dirichlet laplace特征值在球体上的半径较小的球比相同半径的欧几里得球上的相应特征值小。而双曲线空间的Dirichlet Laplace特征值则相反。
In this article we will explore Dirichlet Laplace eigenvalues on balls on spherically symmetric manifolds. We will compare any Dirichlet Laplace eigenvalue with the corresponding Dirichlet Laplace eigenvalue on balls in Euclidean space with the same radius. As a special case we will show that the Dirichlet Laplace eigenvalues on balls with small radius on the sphere are smaller than the corresponding eigenvalues on the Euclidean ball with the same radius. While the opposite is true for the Dirichlet Laplace eigenvalues of hyperbolic spaces.
