Distance comparison principle and Grayson type theorem in the three   dimensional curve shortening flow
  In this paper, we use the distance comparison principle, first been developed by G. Huisken, to study the spatial curve shortening flow. We have got the result that if the initial curve is the helix, then the local minimum of the ratio of the extrinsic and intrinsic distance is non-decreasing. And we have proved a Grayson type theorem for a variety of spatial curves. 
Siming He
math.DG