On uniqueness of tangent cones for Einstein manifolds
  We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section. 
Tobias Holck Colding and William P. Minicozzi II
math.DG math.AG math.AP