The authors consider a family of smooth immersions F（., t） ：M^n→R^n＋1 of closed hypersurfaces in R^n＋1 moving by the mean curvature flow F（p,t）/ t=-H（p,t）.v（p,t） for t E [0, T）. They show that if the norm...The authors consider a family of smooth immersions F（., t） ：M^n→R^n＋1 of closed hypersurfaces in R^n＋1 moving by the mean curvature flow F（p,t）/ t=-H（p,t）.v（p,t） for t E [0, T）. They show that if the norm of the second fundamental form is bounded above by some power of mean curvature and the certain subcritical quantities concerning the mean curvature integral are bounded, then the flow can extend past time T. The result is similar to that in [6-9].展开更多
基金supported by the National Natural Science Foundation of China (Nos.10871069,10871070)the Shanghai Leading Academic Discipline Project (No.B407)
文摘The authors consider a family of smooth immersions F（., t） ：M^n→R^n＋1 of closed hypersurfaces in R^n＋1 moving by the mean curvature flow F（p,t）/ t=-H（p,t）.v（p,t） for t E [0, T）. They show that if the norm of the second fundamental form is bounded above by some power of mean curvature and the certain subcritical quantities concerning the mean curvature integral are bounded, then the flow can extend past time T. The result is similar to that in [6-9].
