Families of non-tiling domains satisfying Pólya's conjecture
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918073729024000 |
|---|---|
| author | Freitas, Pedro Salavessa, Isabel |
| author_facet | Freitas, Pedro Salavessa, Isabel |
| contents | We show the existence of classes of non-tiling domains satisfying Pólya's conjecture in any dimension, in both the Euclidean and non-Euclidean cases. This is a consequence of a more general observation asserting that if a domain satisfies Pólya's conjecture eventually, that is, for a sufficiently large order of the eigenvalues, and may be partitioned into $p$ non-overlapping isometric sub-domains, with $p$ arbitrarily large, then there exists an order $p_{0}$ such that for $p$ larger than $p_{0}$ all such sub-domains satisfy Pólya's conjecture. In particular, this allows us to show that families of sectors of domains of revolution with analytic boundary, and thin cylinders satisfy Pólya's conjecture, for instance. We also improve upon the Li-Yau constant for general cylinders in the Dirichlet case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_08902 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Families of non-tiling domains satisfying Pólya's conjecture Freitas, Pedro Salavessa, Isabel Spectral Theory Analysis of PDEs Differential Geometry 35P15 (Primary), 35J05, 35J25, 35P20 (Secondary) We show the existence of classes of non-tiling domains satisfying Pólya's conjecture in any dimension, in both the Euclidean and non-Euclidean cases. This is a consequence of a more general observation asserting that if a domain satisfies Pólya's conjecture eventually, that is, for a sufficiently large order of the eigenvalues, and may be partitioned into $p$ non-overlapping isometric sub-domains, with $p$ arbitrarily large, then there exists an order $p_{0}$ such that for $p$ larger than $p_{0}$ all such sub-domains satisfy Pólya's conjecture. In particular, this allows us to show that families of sectors of domains of revolution with analytic boundary, and thin cylinders satisfy Pólya's conjecture, for instance. We also improve upon the Li-Yau constant for general cylinders in the Dirichlet case. |
| title | Families of non-tiling domains satisfying Pólya's conjecture |
| topic | Spectral Theory Analysis of PDEs Differential Geometry 35P15 (Primary), 35J05, 35J25, 35P20 (Secondary) |
| url | https://arxiv.org/abs/2204.08902 |