High-energy eigenfunctions of the Laplacian on the torus and the sphere with nodal sets of complicated topology
| Autor: | F. Torres de Lizaur, Daniel Peralta-Salas, Alberto Enciso |
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| Přispěvatelé: | Universidad de Sevilla. Departamento de Análisis Matemático, Universidad de Sevilla. FQM104: Analisis Matematico |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Mathematics - Differential Geometry Spectral theory Inverse localization Torus Eigenfunctions of the Laplacian Contractible space Combinatorics Mathematics - Spectral Theory Nodal sets Hypersurface Mathematics - Analysis of PDEs Integer Differential geometry Differential Geometry (math.DG) FOS: Mathematics Diffeomorphism Isotopy type Laplace operator Spectral Theory (math.SP) Analysis of PDEs (math.AP) |
| Zdroj: | Nonlinear Partial Differential Equations for Future Applications : Sendai, Japan, July 10–28 and October 2–6, 2017 Springer Proceedings in Mathematics & Statistics Nonlinear Partial Differential Equations for Future Applications ISBN: 9789813348219 Digital.CSIC. Repositorio Institucional del CSIC instname |
| Popis: | Let $\Sigma$ be an oriented compact hypersurface in the round sphere $\mathbb{S}^n$ or in the flat torus $\mathbb{T}^n$, $n\geq 3$. In the case of the torus, $\Sigma$ is further assumed to be contained in a contractible subset of $\mathbb{T}^n$. We show that for any sufficiently large enough odd integer $N$ there exists an eigenfunctions $\psi$ of the Laplacian on $\mathbb{S}^n$ or $\mathbb{T}^n$ satisfying $\Delta \psi=-\lambda \psi$ (with $\lambda=N(N+n-1)$ or $N^2$ on $\mathbb{S}^n$ or $\mathbb{T}^n$, respectively), and with a connected component of the nodal set of $\psi$ given by~$\Sigma$, up to an ambient diffeomorphism. Comment: 14 pages. arXiv admin note: text overlap with arXiv:1712.10310, arXiv:1505.01605 |
| Databáze: | OpenAIRE |
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