Quasimode concentration on compact space forms
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916217022840832 |
|---|---|
| author | Huang, Xiaoqi Sogge, Christopher D. |
| author_facet | Huang, Xiaoqi Sogge, Christopher D. |
| contents | We show that the upper bounds for the $L^2$-norms of $L^1$-normalized quasimodes that we obtained in [9] are always sharp on any compact space form. This allows us to characterize compact manifolds of constant sectional curvature using the decay rates of lower bounds of $L^1$-norms of $L^2$-normalized log-quasimodes fully resolving a problem initiated by the second author and Zelditch [15]. We are also able to characterize such manifolds by the concentration of quasimodes near periodic geodesics as measured by $L^2$-norms over thin geodesic tubes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasimode concentration on compact space forms Huang, Xiaoqi Sogge, Christopher D. Analysis of PDEs Classical Analysis and ODEs Differential Geometry 58J50, 35P15 We show that the upper bounds for the $L^2$-norms of $L^1$-normalized quasimodes that we obtained in [9] are always sharp on any compact space form. This allows us to characterize compact manifolds of constant sectional curvature using the decay rates of lower bounds of $L^1$-norms of $L^2$-normalized log-quasimodes fully resolving a problem initiated by the second author and Zelditch [15]. We are also able to characterize such manifolds by the concentration of quasimodes near periodic geodesics as measured by $L^2$-norms over thin geodesic tubes. |
| title | Quasimode concentration on compact space forms |
| topic | Analysis of PDEs Classical Analysis and ODEs Differential Geometry 58J50, 35P15 |
| url | https://arxiv.org/abs/2404.13738 |