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SCALAR CURVATURE OF HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN SPHERES

  • QIN ZHANG (a1)
Abstract

Let Mn be an n-dimensional closed hypersurface with constant mean curvature H satisfying |H| ≤ ϵ(n) in a unit sphere Sn+1(1), n ≤ 8 and S the square of the length of the second fundamental form of M. There exists a constant δ(n, H) > 0, which depends only on n and H such that if S0 ≤ S ≤ S0 + δ(n, H), then S ≡ S0 and M is isometric to a Clifford hypersurface, where ϵ(n) is a sufficiently small constant depending on n and .

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COPYRIGHT: © Glasgow Mathematical Journal Trust 2011
References
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
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