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An estimate of the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere
Authors:Hongcang Yang  Qing-Ming Cheng
Institution:(1) Institute of Mathematics, Academia Sinica, 100080 Beijing, P.R.China;(2) Institute of Mathematics, Fudan University, 200433 Shanghai, P.R. China
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] The second author's research was supported by NNSFC, FECC and CPSF.
Keywords:minimal hypersurface  second fundamental form and scalar curvature
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