Abstract
AbstractIn this article we will explore Dirichlet Laplace eigenvalues of balls with spherically symmetric metrics. We will compare any Dirichlet Laplace eigenvalue with the corresponding Dirichlet Laplace eigenvalue on balls in Euclidean space with the same radii. As a special case we shall show that the Dirichlet Laplace eigenvalues of balls with small radii on the sphere are smaller than the corresponding eigenvalues of the Euclidean balls with the same radii. The opposite correspondence is true for the Dirichlet Laplace eigenvalues of hyperbolic spaces.
Funder
Gottfried Wilhelm Leibniz Universität Hannover
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Algebra and Number Theory,Analysis
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