English

Distance comparison principle and Grayson type theorem in the three dimensional curve shortening flow

Differential Geometry 2012-09-25 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1209.5146,
  title  = {Distance comparison principle and Grayson type theorem in the three dimensional curve shortening flow},
  author = {Siming He},
  journal= {arXiv preprint arXiv:1209.5146},
  year   = {2012}
}

Comments

15 pages, undergraduate thesis