Entire hypersurfaces of constant scalar curvature in Minkowski space
| Autor: | Bayard, Pierre, Seppi, Andrea |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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-B\'eguin-Zeghib (for $n=2$) and Smith (for $n=3$). Comment: 30 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|