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Archiv der Mathematik

, Volume 87, Issue 1, pp 60–71 | Cite as

On complete noncompact submanifolds with constant mean curvature and finite total curvature in Euclidean spaces

  • Senlin Xu
  • Qintao Deng
Original Paper

Abstract.

In this paper, we consider a complete noncompact n-submanifold M with parallel mean curvature vector h in an Euclidean space. If M has finite total curvature, we prove that M must be minimal, so that M is an affine n-plane if it is strongly stable. This is a generalization of the result on strongly stable complete hypersurfaces with constant mean curvature in \(\mathbb{R}^{n+1}.\)

Mathematics Subject Classification (2000).

53C40 53C42 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsCentral China Normal UniversityWuhanP.R. China

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