Eigenvalues on Spherically Symmetric Manifolds

Stine Marie Berge

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arXiv · 2203.11911

Eigenvalues on Spherically Symmetric Manifolds

Stine Marie Berge

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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.

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BibTeX RIS

Stine Marie Berge. 2022-03-22. Eigenvalues on Spherically Symmetric Manifolds. https://arxiv.org/abs/2203.11911

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