Entire hypersurfaces of constant scalar curvature in Minkowski space
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914916582031360 |
|---|---|
| author | Bayard, Pierre Seppi, Andrea |
| author_facet | Bayard, Pierre Seppi, Andrea |
| contents | We show that every regular domain $\mathcal D$ in Minkowski space $\mathbb R^{n,1}$ which is not a wedge admits an entire hypersurface whose domain of dependence is $\mathcal D$ and whose scalar curvature is a prescribed constant (or function, under suitable hypotheses) in $(-\infty,0)$. Under rather general assumptions, these hypersurfaces are unique and provide foliations of $\mathcal D$. As an application, we show that every maximal globally hyperbolic Cauchy compact flat spacetime admits a foliation by hypersurfaces of constant scalar curvature, generalizing to any dimension previous results of Barbot-Béguin-Zeghib (for $n=2$) and Smith (for $n=3$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10042 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entire hypersurfaces of constant scalar curvature in Minkowski space Bayard, Pierre Seppi, Andrea Differential Geometry 53A07, 53C42, 53C50, 35J60 We show that every regular domain $\mathcal D$ in Minkowski space $\mathbb R^{n,1}$ which is not a wedge admits an entire hypersurface whose domain of dependence is $\mathcal D$ and whose scalar curvature is a prescribed constant (or function, under suitable hypotheses) in $(-\infty,0)$. Under rather general assumptions, these hypersurfaces are unique and provide foliations of $\mathcal D$. As an application, we show that every maximal globally hyperbolic Cauchy compact flat spacetime admits a foliation by hypersurfaces of constant scalar curvature, generalizing to any dimension previous results of Barbot-Béguin-Zeghib (for $n=2$) and Smith (for $n=3$). |
| title | Entire hypersurfaces of constant scalar curvature in Minkowski space |
| topic | Differential Geometry 53A07, 53C42, 53C50, 35J60 |
| url | https://arxiv.org/abs/2408.10042 |