Acta Mathematica Sinica

, Volume 15, Issue 4, pp 555–560

On the isometric minimal immersion into a euclidean space

  • Qing Chen

DOI: 10.1007/s10114-999-0087-z

Cite this article as:
Chen, Q. Acta Math Sinica (1999) 15: 555. doi:10.1007/s10114-999-0087-z


We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space. A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-positively curved minimal hypersurfaces in a Euclidean space is given.


Minimal immersion Geodesic ball Volume growth Ruled submanifolds 

1991MR Subject Classification

53A20 53C42 

Copyright information

© Springer-Verlag Singapore Pte. Ltd 1999

Authors and Affiliations

  • Qing Chen
    • 1
  1. 1.Department of MathematicsThe University of Science and Technology of ChinaHefeiP. R. China

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