高余维平均曲率流在第一奇异时间处的平均曲率

Mean Curvature at the First Singular Time of the Mean Curvature Flow in Higher Codimension

考虑沿平均曲率向量移动的一族光滑浸入X(.,t):Mm→Rn,满足tX(x,t)=H(x,t),t∈[0,T).证明了:在第一奇异时间T处,若奇异点为第一型的,则平均曲率在T处爆破.

A family of smooth immersions X（·,t）：Mm→Rn of submanifolds in Rn moving by the mean curvature vector /tX（x,t）=H（x,t） for t∈[0,T） was considered.The mean curvature blows up at the first singular time T if all the singularities are of type I.