Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912119778181120 |
|---|---|
| author | Chai, Xiaoxiang Wan, Xueyuan |
| author_facet | Chai, Xiaoxiang Wan, Xueyuan |
| contents | In odd dimensions, we prove a scalar curvature rigidity for parabolic convex polytopes in hyperbolic space enclosed by linear planes in the Poincare upper half-space model and convex with respect to the conformally related flat metric. Our method is based on spinor techniques and relies on the recent smoothing constructions of Brendle-Wang. We also prove a Llarull type rigidity for bounded smooth parabolic convex domains and a dihedral rigidity for polytopal initial data sets with dominant energy conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16022 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space Chai, Xiaoxiang Wan, Xueyuan Differential Geometry General Relativity and Quantum Cosmology 53C24, 52B11, 15A66 In odd dimensions, we prove a scalar curvature rigidity for parabolic convex polytopes in hyperbolic space enclosed by linear planes in the Poincare upper half-space model and convex with respect to the conformally related flat metric. Our method is based on spinor techniques and relies on the recent smoothing constructions of Brendle-Wang. We also prove a Llarull type rigidity for bounded smooth parabolic convex domains and a dihedral rigidity for polytopal initial data sets with dominant energy conditions. |
| title | Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space |
| topic | Differential Geometry General Relativity and Quantum Cosmology 53C24, 52B11, 15A66 |
| url | https://arxiv.org/abs/2312.16022 |