Annals of Global Analysis and Geometry

, Volume 34, Issue 1, pp 55–68 | Cite as

Stability of area-preserving variations in space forms

  • Yijun He
  • Haizhong LiEmail author
Original Paper


In this article, we deal with compact hypersurfaces without boundary immersed in space forms with \(\frac{S_{r+1}}{S_1} = {\rm constant}\) . They are critical points for an area-preserving variational problem. We show that they are r-stable if and only if they are totally umbilical hypersurfaces.


rth mean curvatures r-stability Area-preserving variation 

Mathematics Subject Classification (2000)

Primary 53C42 53A30 Secondary 53B25 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanxi UniversityTaiyuanP.R. China
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingP.R. China

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