L² harmonic 1-forms on minimal submanifolds in hyperbolic space

2010/07/05 by Keomkyo Seo, Seo, Keomkyo
Mathematics · #53C42 #58C40 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #msc:53C42 #msc:58C40

paper · pdf · doi:10.48550/arxiv.1007.0663

6 pages, to appear in Journal of Mathematical Analysis and Applications

arxiv created 2010/07/05 · openalex publication_date 2010/07/05 · arxiv updated 2010/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the nonexistence of L² harmonic 1-forms on a complete super stable minimal submanifold M in hyperbolic space under the assumption that the first eigenvalue λ₁ (M) for the Laplace operator on M is bounded below by (2n-1)(n-1). Moreover, we provide sufficient conditions for minimal submanifolds in hyperbolic space to be super stable.

Related

• Stable minimal hypersurfaces in the hyperbolic space
• Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature
• Rigidity and stability estimates for minimal submanifolds in the\n hyperbolic space
• L² Harmonic 1-forms on submanifolds with finite total curvature
• L²-harmonic p-forms on submanifolds with finite total curvature