A Stability Criterion for Nonparametric Minimal Submanifolds

2002/11/01 by Yng-Ing Lee, Mu-Tao Wang, Mu‐Tao Wang +2
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.math/0211018

submitted

arxiv created 2002/11/01 · openalex publication_date 2002/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An n dimensional minimal submanifold Σ of \R^n+m is called non-parametric if Σ can be represented as the graph of a vector-valued function f:D⊂ \Rⁿ ↦ \R^m. This note provides a sufficient condition for the stability of such Σ in terms of the norm of the differential df.

Citations

• Minimal Varieties in Riemannian Manifolds

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