Uniqueness of Self-similar Shrinkers with Asymptotically Conical Ends

Here H = div (n) is the mean curvature, n is the outward unit normal, x is the position vector and 〈, 〉 denotes the Euclidean inner product. One reason that selfshrinking solutions to the mean curvature flow are particularly interesting is that they provide singularity models of the flow; see [20, 21], [24] and [46]. Throughout, O is the origin of R; BR denotes the open ball in R n+1 centered at O with radius R and SR = ∂BR; DR denotes the open disk in R n×{0} centered at the origin with radius R. We say that C ⊂ R is a regular cone with vertex at O, if