manuscripta mathematica

, Volume 112, Issue 2, pp 161–169

A stability criterion for nonparametric minimal submanifolds


DOI: 10.1007/s00229-003-0404-2

Cite this article as:
Lee, YI. & Wang, MT. manuscripta math. (2003) 112: 161. doi:10.1007/s00229-003-0404-2


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

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsNational Taiwan UniversityTaiwan
  2. 2.Department of MathematicsColumbia UniversityU.S.A