UNIQUENESS OF SELF-SIMILAR SHRINKERS WITH ASYMPTOTICALLY CONICAL ENDS

摘要

Self-shrinkers are a special class of solutions to the mean curvature?ow in Rn+1, which a later time slice is a scaled down copy of an earlier slice. More precisely, hypersurfaceΣinRn+1is said to be a self-shrinker if it satis?es (1.1)H = 1/2. Here H = div (n)isthemeancurvature,n is the outward unit normal, x is the position vector and 〈, 〉 denotes the Euclidean inner product. One reason that self-shrinking solutions to the mean curvature ?ow are particularly interesting is that they provide singularity models of the ?ow; see [20,21], [24] and [48].