Alexandrov's Patchwork and the Bonnet--Myers Theorem for Lorentzian length spaces
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_ | 1866912366868824064 |
|---|---|
| author | Beran, Tobias Napper, Lewis Rott, Felix |
| author_facet | Beran, Tobias Napper, Lewis Rott, Felix |
| contents | We present several key results for Lorentzian pre-length spaces with global timelike curvature bounds. Most significantly, we construct a Lorentzian analogue to Alexandrov's Patchwork, thus proving that suitably nice Lorentzian pre-length spaces with local upper timelike curvature bound also satisfy a corresponding global upper bound. Additionally, for spaces with global lower bound on their timelike curvature, we provide a Bonnet--Myers style result, constraining their finite diameter. Throughout, we make the natural comparisons to the metric case, concluding with a discussion of potential applications and ongoing work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11615 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Alexandrov's Patchwork and the Bonnet--Myers Theorem for Lorentzian length spaces Beran, Tobias Napper, Lewis Rott, Felix Differential Geometry Mathematical Physics Metric Geometry 53C50, 53C23, 53B30, 51K10 We present several key results for Lorentzian pre-length spaces with global timelike curvature bounds. Most significantly, we construct a Lorentzian analogue to Alexandrov's Patchwork, thus proving that suitably nice Lorentzian pre-length spaces with local upper timelike curvature bound also satisfy a corresponding global upper bound. Additionally, for spaces with global lower bound on their timelike curvature, we provide a Bonnet--Myers style result, constraining their finite diameter. Throughout, we make the natural comparisons to the metric case, concluding with a discussion of potential applications and ongoing work. |
| title | Alexandrov's Patchwork and the Bonnet--Myers Theorem for Lorentzian length spaces |
| topic | Differential Geometry Mathematical Physics Metric Geometry 53C50, 53C23, 53B30, 51K10 |
| url | https://arxiv.org/abs/2302.11615 |