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arXiv · 2408.10042

Entire hypersurfaces of constant scalar curvature in Minkowski space

Pierre Bayard·Andrea Seppi
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Abstract

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 $n=3$).

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Pierre Bayard, Andrea Seppi. 2024-08-19. Entire hypersurfaces of constant scalar curvature in Minkowski space. https://arxiv.org/abs/2408.10042

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