A characterization of Clifford hypersurfaces among embedded constant mean curvature hypersurfaces in a unit sphere

2017 ◽  
Vol 24 (2) ◽  
pp. 503-534 ◽  
Author(s):  
Sung-Hong Min ◽  
Keomkyo Seo
Keyword(s):  
Unit Sphere ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Hypersurfaces

scholarly journals CONSTANT MEAN CURVATURE HYPERSURFACES IN SPHERES

2011 ◽  
Vol 54 (1) ◽  
pp. 77-86 ◽  
Author(s):  
QIN-TAO DENG ◽  
HUI-LING GU ◽  
YAN-HUI SU
Keyword(s):  
Scalar Curvature ◽  
Unit Sphere ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Hypersurfaces ◽  
Small Constant ◽  
Closed Hypersurfaces ◽  
Hypersurfaces In Spheres

AbstractIn 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.

scholarly journals Gauss map and the topology of constant mean curvature hypersurfaces of $$\mathbb {S}^{7}$$ and $$\mathbb {CP}^{3}$$

2019 ◽  
Vol 163 (1-2) ◽  
pp. 279-290
Author(s):  
Fidelis Bittencourt ◽  
Pedro Fusieger ◽  
Eduardo R. Longa ◽  
Jaime Ripoll
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Gauss Map ◽  
Constant Mean Curvature Hypersurfaces

scholarly journals Stable constant mean curvature hypersurfaces

2007 ◽  
Vol 135 (10) ◽  
pp. 3359-3367 ◽  
Author(s):  
Maria Fernanda Elbert ◽  
Barbara Nelli ◽  
Harold Rosenberg
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Hypersurfaces
Sign in / Sign up

Export Citation Format

Share Document