دورية
Exponential localization of Steklov eigenfunctions on warped product manifolds: the flea on the elephant phenomenon
| العنوان: | Exponential localization of Steklov eigenfunctions on warped product manifolds: the flea on the elephant phenomenon |
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| المؤلفون: | Daudé, Thierry, Helffer, Bernard, Nicoleau, François |
| المصدر: | Annales mathématiques du Québec; 20210101, Issue: Preprints p1-36, 36p |
| مستخلص: | This paper is devoted to the analysis of Steklov eigenvalues and Steklov eigenfunctions on a class of warped product Riemannian manifolds (M, g) whose boundary ∂Mconsists in two distinct connected components Γ0and Γ1. First, we show that the Steklov eigenvalues can be divided into two families (λm±)m≥0which satisfy accurate asymptotics as m→∞. Second, we consider the associated Steklov eigenfunctions which are the harmonic extensions of the boundary Dirichlet to Neumann eigenfunctions. In the case of symmetric warped product, we prove that the Steklov eigenfunctions are exponentially localized on the whole boundary ∂Mas m→∞. When we add an asymmetric perturbation of the metric to a symmetric warped product, we observe in almost all cases a flea on the elephant effect. Roughly speaking, we prove that “half” the Steklov eigenfunctions are exponentially localized on one connected component of the boundary, say Γ0, and the other half on the other connected component Γ1as m→∞. |
| قاعدة البيانات: | Supplemental Index |
| تدمد: | 21954755 21954763 |
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| DOI: | 10.1007/s40316-021-00185-3 |