Work

Entire hypersurfaces of constant scalar curvature in Minkowski space

Year: 2025

Type: article

Abstract: We show that every regular domain 𝒟 in Minkowski space R n , 1 \mathbb{R}^{n,1} which is not a wedge admits an entire hypersurface whose domain of dependence is 𝒟 and whose scalar curvature is a prescribed constant (or function, under suitable hypotheses) in ( − ∞ , 0 ) (-\infty,0) . Under rather general assumptions, these hypersurfaces are unique and provide foliations of 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 n=2 ) and Smith (for n = 3 n=3 ).

Source: Journal für die reine und angewandte Mathematik (Crelles Journal)

DOI: 10.1515/crelle-2025-0023

Authors: Pierre Bayard, Andrea Seppi

Institutions: Universidad Nacional Autónoma de México, University of Turin

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funders: European Commission, European Research Council