Abstract
LetM n (n>3) be a closed minimal hypersurface with constant scalar curvature in the unit sphereS n+1(1) andS the square of the length of its second fundamental form. In this paper we prove thatS>n implies estimates of the formS>n+cn−d withc≥1/4. For example, forn>17 andS>n we proveS>n+1/4n which is sharper than a recent result of the authors [5]
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The second author's research was supported by NNSFC, FECC and CPSF.
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Yang, H., Cheng, QM. An estimate of the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere. Manuscripta Math 84, 89–100 (1994). https://doi.org/10.1007/BF02567445
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DOI: https://doi.org/10.1007/BF02567445