English

On the noncollapsedness of positively curved Type I ancient Ricci flows

Differential Geometry 2021-02-09 v1

Abstract

In this article, we study complete Type I ancient Ricci flows with positive sectional curvature. Our main results are as follows: in the complete and noncompact case, all such ancient solutions must be noncollapsed on all scales; in the closed case, if the dimension is even, then all such ancient solutions must be noncollapsed on all scales. This furthermore gives a complete classification for three-dimensional noncompact Type I ancient solutions without assuming the noncollapsing condition.

Keywords

Cite

@article{arxiv.2102.03508,
  title  = {On the noncollapsedness of positively curved Type I ancient Ricci flows},
  author = {Liang Cheng and Yongjia Zhang},
  journal= {arXiv preprint arXiv:2102.03508},
  year   = {2021}
}