A Liouville-type theorem for stable minimal hypersurfaces

2021/01/16 by Leon Simon, Simon, Leon · 2 citations
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.2101.06404

openalex publication_date 2021/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if M is a strictly stable complete minimal hypersurface in Euclidean space with finite density at infinity and which lies on one side of a minimal cylinder with cross-section a strictly stable area minimizing hypercone, then M must be cylindrical. Applications will be given in the references [Sim20a], [Sim20b].

Cited by

• Minimal surfaces and comparison geometry
• Harmonic functions on minimal submanifold with cylindrical cone

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