Boundedness of the number of nodal domains for eigenfunctions of generic Kaluza–Klein 3-folds
| Autor: | Junehyuk Jung, Steve Zelditch |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Basis (linear algebra) Riemann surface 010102 general mathematics Kaluza–Klein theory Mathematics::Spectral Theory Eigenfunction 01 natural sciences Action (physics) symbols.namesake 0103 physical sciences symbols Orthonormal basis 010307 mathematical physics Geometry and Topology 0101 mathematics Invariant (mathematics) Laplace operator Mathematics |
| Zdroj: | Annales de l'Institut Fourier. 70:971-1027 |
| ISSN: | 1777-5310 |
| DOI: | 10.5802/aif.3329 |
| Popis: | This article concerns the number of nodal domains of eigenfunctions of the Laplacian on special Riemannian $3$-manifolds, namely nontrivial principal $S^1$ bundles $P \to X$ over Riemann surfaces equipped with certain $S^1$ invariant metrics, the Kaluza-Klein metrics. We prove for generic Kaluza-Klein metrics that any Laplacian eigenfunction has exactly two nodal domains unless it is invariant under the $S^1$ action. We also construct an explicit orthonormal eigenbasis on the flat $3$-torus $\mathbb{T}^3$ for which every non-constant eigenfunction belonging to the basis has two nodal domains. |
| Databáze: | OpenAIRE |
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