Blow up of Subcritical Quantities at the First Singular Time of the Mean Curvature Flow
نویسنده
چکیده
Consider a family of smooth immersions F (·, t) : M → R of closed hypersurfaces in R moving by the mean curvature flow ∂F (p,t) ∂t = −H(p, t) ·ν(p, t), for t ∈ [0, T ). We show that at the first singular time of the mean curvature flow, certain subcritical quantities concerning the second fundamental form, for example ∫ t 0 ∫ Ms |A| log(2+|A|)dμds, blow up. Our result is a log improvement of recent results of Le-Sesum, Xu-Ye-Zhao where the scaling invariant quantities were considered.
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