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[1] Wang Peijun, Chao Xiaoli,. Hypersurfaces with constant mean curvature in unit sphere [J]. Journal of Southeast University (English Edition), 2016, 32 (1): 132-134. [doi:10.3969/j.issn.1003-7985.2016.01.022]
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
32
Issue:
2016 1
Page:
132-134
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2016-03-20

Info

Title:
Hypersurfaces with constant mean curvature in unit sphere
Author(s):
Wang Peijun Chao Xiaoli
Department of Mathematics, Southeast University, Nanjing 210096, China
Keywords:
hypersurface with constant mean curvature unit sphere pinching
PACS:
O186.1
DOI:
10.3969/j.issn.1003-7985.2016.01.022
Abstract:
The pinching of n-dimensional closed hypersurface M with constant mean curvature H in unit sphere Sn+11(1)is considered. Let(~overA)=∑i, j, kh2ijk(λi+nH)2, (~overB)=∑i, j, kh2ijk(λi+nH)·(λj+nH), (~overS)=∑i(λi+nH)2, where hijiδij. Utilizing Lagrange’s method, a sharper pointwise estimation of 3((~overA)-2(~overB))in terms of (~overS) and ∇h2 is obtained, here ∇h2=∑i, j, kh2ijk2. Then, with the help of this, it is proved that M is isometric to the Clifford hypersurface if the square norm of the second fundamental form of M satisfies certain conditions. Hence, the pinching result of the minimal hypersurface is extended to the hypersurface with constant mean curvature case.

References:

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Memo

Memo:
Biographies: Wang Peijun(1989—), male, graduate; Chao Xiaoli(corresponding author), male, doctor, professor, xlchao@seu.edu.cn.
Citation: Wang Peijun, Chao Xiaoli. Hypersurfaces with constant mean curvature in unit sphere[J].Journal of Southeast University(English Edition), 2016, 32(1):132-134. DOI:10.3969/j.issn.1003-7985.2016.01.022.
Last Update: 2016-03-20