Stability and rigidity results of space-like hypersurface in the Minkowski space

2025/06/01 by Jianhua Chen, Chen, Jianhua, Haiyun Deng +5
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.2506.01012

openalex publication_date 2025/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish some rigidity theorems for space-like hypersurfaces in Minkowski space by using a Weinberger-type approach with P-functions and integral identities. Firstly, for space-like hypersurfaces M represented as graphs x_n+1=u(x) over domain Ω⊂\mathbb Rⁿ, if higher-order mean curvature ratio \fracH_kH_l(l

Citations

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• Hölder stability for Serrin's overdetermined problem
• Serrin-Type Overdetermined Problems: an Alternative Proof
• A symmetry problem in potential theory
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Related

• Rigidity of spacelike hypersurface with constant curvature and intersection angle condition
• Stability of Hypersurfaces in Minkowsky Normed Spaces
• Weighted Hsiung-Minkowski formulas and rigidity of umbilical hypersurfaces
• Rigidity theorems of the space-like λ-hypersurfaces in the Lorentzian space \mathbb Rⁿ⁺¹₁
• A Rigidity Theorem for Spacelike Hypersurfaces in de Sitter Space