In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental f...In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental form and the mean curvature. We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval.This improved the relative results of M. Okumura,Shen Yibihg and Sun Ziqi,etc.展开更多
In this paper, a rigidity theorem of hypersurface in real space form will be given. In addition, we obtain rigidity theorems of submanifold in sphere which improve the result of Hou and Xu.
A class of curvature estimates of spacelike admissible hypersurfaces related to translating solitons of the higher order mean curvature flow in the Minkowski space is ob- tained, which may offer an idea to study an op...A class of curvature estimates of spacelike admissible hypersurfaces related to translating solitons of the higher order mean curvature flow in the Minkowski space is ob- tained, which may offer an idea to study an open question of the existence of hypersurfaces with the prescribed higher mean curvature in the Minkowski space.展开更多
文摘In this paper,we study the pinching problem for a hypersurface with constant mean curvature in space forms to be totally umbilical by osing the relationship between the square of the length of the second fundamental form and the mean curvature. We obtained a best pinching interval and decided the complete classification of hypersurfaces at the terminal of the interval.This improved the relative results of M. Okumura,Shen Yibihg and Sun Ziqi,etc.
文摘In this paper, a rigidity theorem of hypersurface in real space form will be given. In addition, we obtain rigidity theorems of submanifold in sphere which improve the result of Hou and Xu.
基金the National Natural Science Foundation of China(No.11001261)
文摘A class of curvature estimates of spacelike admissible hypersurfaces related to translating solitons of the higher order mean curvature flow in the Minkowski space is ob- tained, which may offer an idea to study an open question of the existence of hypersurfaces with the prescribed higher mean curvature in the Minkowski space.