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In this paper, we show that if the mean curvature of a closed smooth embeddedmean curvature flow in R^3 is of type-I, then the rescaled flow at the firstfinite singular time converges smoothly to a self-shrinker flow withmultiplicity one. This result confirms Ilmanen's multiplicity-one conjectureunder the assumption that the mean curvature is of type-I. As a corollary, weshow that the mean curvature at the first singular time of a closed smoothembedded mean curvature flow in R^3 is at least of type-I.

On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-I mean curvature