摘要
In this paper,the authors consider a family of smooth immersions Ft : Mn→Nn+1of closed hypersurfaces in Riemannian manifold Nn+1with bounded geometry,moving by the Hkmean curvature flow.The authors show that if the second fundamental form stays bounded from below,then the Hkmean curvature flow solution with finite total mean curvature on a finite time interval [0,Tmax)can be extended over Tmax.This result generalizes the extension theorems in the paper of Li(see "On an extension of the Hkmean curvature flow,Sci.China Math.,55,2012,99–118").
In this paper, the authors consider a family of smooth immersions Ft ： Mn → Nn＋1 of closed hypersurfaces in Riemannian manifold Nn＋1 with bounded geometry, mov- ing by the Hk mean curvature flow. The authors show that if the second fundamental form stays bounded from below, then the Hk mean curvature flow solution with finite total mean curvature on a finite time interval [0, Tmax） can be extended over Tmax. This result gen- eralizes the extension theorems in the paper of Li （see ＂On an extension of the Hk mean curvature flow, Sci. China Math, 55, 2012, 99-118＂）.
基金
supported by the National Natural Science Foundation of China(Nos.11301399,11126189,11171259,11126190)
the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120141120058)
the China Postdoctoral Science Foundation(No.20110491212)
the Fundamental Research Funds for the Central Universities(Nos.2042011111054,20420101101025)
