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A stability criterion for nonparametric minimal submanifolds

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Abstract.

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.

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Authors and Affiliations

  1. Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan

    Yng-Ing Lee

  2. Department of Mathematics, Columbia University, New York NY, 10027, U.S.A

    Mu-Tao Wang

Authors
  1. Yng-Ing Lee
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  2. Mu-Tao Wang
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Corresponding author

Correspondence to Yng-Ing Lee.

Additional information

The first author is partially supported by National Science Council, Taiwan, NSC 90-2115-M-002-009 and NSC 91-2115-M-002-004. The second author is partially supported by National Science Foundation, DMS 0104163.

Mathematics Subject Classification (2000): 49Q05, 53A07, 53C38, 53C42

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Lee, YI., Wang, MT. A stability criterion for nonparametric minimal submanifolds. manuscripta math. 112, 161–169 (2003). https://doi.org/10.1007/s00229-003-0404-2

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  • DOI: https://doi.org/10.1007/s00229-003-0404-2

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