Stability of area-preserving variations in space forms |
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| Authors: | Yijun He Haizhong Li |
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| Institution: | (1) School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, P.R. China;(2) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P.R. China |
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| Abstract: | In this article, we deal with compact hypersurfaces without boundary immersed in space forms with  . 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.
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| Keywords: | rth mean curvatures r-stability Area-preserving variation |
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