Abstract
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.
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He, Y., Li, H. Stability of area-preserving variations in space forms. Ann Glob Anal Geom 34, 55–68 (2008). https://doi.org/10.1007/s10455-007-9095-3
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DOI: https://doi.org/10.1007/s10455-007-9095-3