  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.
