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SCALAR CURVATURE OF HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN SPHERES

Published online by Cambridge University Press:  02 August 2011

QIN ZHANG
QIN ZHANG*
Affiliation:
Institute of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China e-mail: [email protected]
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Abstract

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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 .

Keywords

Primary 53C4253B25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 67 - 75
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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