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Bernstein type theorems with flat normal bundle

Calculus of Variations and Partial Differential Equations volume 26, pages 57–67 (2006)Cite this article

Abstract

We prove Bernstein type theorems for minimal n-submanifolds in ℝn+p with flat normal bundle. Those are natural generalizations of the corresponding results of Ecker-Huisken and Schoen-Simon-Yau for minimal hypersurfaces.

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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences Inselstr. 22-26, 04103, Leipzig, Germany

    Knut Smoczyk

  2. Institute of Mathematics, Fudan University Shanghai, China and Max Planck Institute for Mathematics in the Sciences Inselstr. 22-26, 04103, Leipzig, Germany

    Guofang Wang

  3. Institute of Mathematics Fudan University, Shanghai, China

    Y. L. Xin

Authors
  1. Knut Smoczyk
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  2. Guofang Wang
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  3. Y. L. Xin
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Corresponding author

Correspondence to Knut Smoczyk.

Additional information

The research of the first author was supported by a Heisenberg fellowship of the DFG

The research of the third author was partially supported by project # 973 of MSTC and SFECC

Mathematics Subject Classification Primary (2000) 53C42

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Smoczyk, K., Wang, G. & Xin, Y.L. Bernstein type theorems with flat normal bundle. Calc. Var. 26, 57–67 (2006). https://doi.org/10.1007/s00526-005-0359-0

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  • DOI: https://doi.org/10.1007/s00526-005-0359-0

Keywords

  • System Theory
  • Natural Generalization
  • Normal Bundle
  • Type Theorem
  • Minimal Hypersurface