Entire spacelike hypersurfaces with constant σ_n-1 curvature in Minkowski space

2020/05/13 by Changyu Ren, Zhizhang Wang, Ren, Changyu +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2005.06109

openalex publication_date 2020/05/13 · openalex created_date 2020/05/21 · openalex updated_date 2026/07/28

Abstract

We prove that, in Minkowski space, if a spacelike, (n-1)-convex hypersurface M with constant σ_n-1 curvature has bounded principal curvatures, then M is convex. Moreover, if M is not strictly convex, after an ℝ^n,1 rigid motion, M splits as a product M^n-1×ℝ. We also construct nontrivial examples of strictly convex, spacelike hypersurface M with constant σ_n-1 curvature and bounded principal curvatures.

Citations

• Differential equations on riemannian manifolds and their geometric applications
• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian
• Global C2‐Estimates for Convex Solutions of Curvature Equations

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• Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds

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