An estimate of the pinching constant of minimal hypersurfaces with constant scalar curvature in the unit sphere |
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Authors: | Hongcang Yang Qing-Ming Cheng |
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Institution: | (1) Institute of Mathematics, Academia Sinica, 100080 Beijing, P.R.China;(2) Institute of Mathematics, Fudan University, 200433 Shanghai, P.R. China |
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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. |
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Keywords: | minimal hypersurface second fundamental form and scalar curvature |
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