Eigenvalues on Spherically Symmetric Manifolds

2022/03/22 by Stine Marie Berge, Berge, Stine Marie
Computer Science · Mathematics · #35J05 #58J50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2203.11911

openalex publication_date 2022/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• The spectrum of geodesic balls on spherically symmetric manifolds
• A note on the first eigenvalue of spherically symmetric manifolds
• A second eigenvalue bound for the Dirichlet Laplacian in hyperbolic space
• Eigenvalue gaps for the Laplacian on hypersurfaces of the sphere
• An isoperimetric inequality for Laplace eigenvalues on the sphere