Geodesic
CONSTANT MEAN CURVATURE HYPERSURFACES IN SPHERES
Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 77-86

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we first summarise the progress for the famous Chern conjecture, and then we consider n-dimensional closed hypersurfaces with constant mean curvature H in the unit sphere n+1 with n ≤ 8 and generalise the result of Cheng et al. (Q. M. Cheng, Y. J. He and H. Z. Li, Scalar curvature of hypersurfaces with constant mean curvature in a sphere, Glasg. Math. J. 51(2) (2009), 413–423). In order to be precise, we prove that if |H| ≤ ε(n), then 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 the Clifford hypersurface, where ε(n) is a sufficiently small constant depending on n.
DOI : 10.1017/S001708951100036X
Mots-clés : 53C40, 53C42 
DENG, QIN-TAO; GU, HUI-LING; SU, YAN-HUI. CONSTANT MEAN CURVATURE HYPERSURFACES IN SPHERES. Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 77-86. doi: 10.1017/S001708951100036X
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