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

DOI

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
@article{10_1017_S001708951100036X,
     author = {DENG, QIN-TAO and GU, HUI-LING and SU, YAN-HUI},
     title = {CONSTANT {MEAN} {CURVATURE} {HYPERSURFACES} {IN} {SPHERES}},
     journal = {Glasgow mathematical journal},
     pages = {77--86},
     year = {2012},
     volume = {54},
     number = {1},
     doi = {10.1017/S001708951100036X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951100036X/}
}
TY  - JOUR
AU  - DENG, QIN-TAO
AU  - GU, HUI-LING
AU  - SU, YAN-HUI
TI  - CONSTANT MEAN CURVATURE HYPERSURFACES IN SPHERES
JO  - Glasgow mathematical journal
PY  - 2012
SP  - 77
EP  - 86
VL  - 54
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708951100036X/
DO  - 10.1017/S001708951100036X
ID  - 10_1017_S001708951100036X
ER  - 
%0 Journal Article
%A DENG, QIN-TAO
%A GU, HUI-LING
%A SU, YAN-HUI
%T CONSTANT MEAN CURVATURE HYPERSURFACES IN SPHERES
%J Glasgow mathematical journal
%D 2012
%P 77-86
%V 54
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708951100036X/
%R 10.1017/S001708951100036X
%F 10_1017_S001708951100036X

Cité par Sources :