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
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摘要: 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Abstract: 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
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