vix.ing · top · new · best · stats · spec

On the noncollapsedness of positively curved Type I ancient Ricci flows

2021/02/06 by Cheng, Liang, Zhang, Yongjia
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.03508

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.

Related