L~2-harmonic forms and stable hypersurfaces in space forms

摘要

We prove that a complete noncompact orientable stable minimal hypersurface in S~(n+1) (n ≤ 4) admits no nontrivial L~2-harmonic forms. We also obtain that a complete noncompact strongly stable hypersurface with constant mean curvature in R~(n+1) or S~(n+1) (n ≤ 4) admits no nontrivial L~2-harmonic forms. These results are generalized versions of Tanno's result on stable minimal hypersurfaces in Rn+1.