6 papers
A gap theorem for metric solitons and its applications
Ganqi Wang, Yongjia Zhang
In this paper, we prove a gap theorem for -limit metric solitons with respect to the asymptotic volume ratio (AVR): if the AVR of a metric soliton is sufficiently close…
Ancient Ricci flows with nonnegative Ricci curvature
Yuxing Deng, Ganqi Wang, Yongjia Zhang
In this paper, we study the asymptotic geometry of a noncollapsed ancient Ricci flow with nonnegative Ricci curvature via its tangent flow at infinity -- a noncollapsed $\mathbb{F}…
An -regularity theorem for Perelman's reduced volume
Liang Cheng, Yongjia Zhang
In this article, we prove an -regularity theorem for Perelman's reduced volume. We show that on a Ricci flow, if Perelman's reduced volume is close to , then the curvature ra…
On noncollapsed -limit metric solitons
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
A noncollapsed -limit metric soliton is a self-similar singularity model that inevitably arises when studying the Ricci flow with the tool of -convergence […
Dimension Reduction for Positively Curved Steady Solitons
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
We consider noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature. We show that such solitons always dimension reduce at infinity. This generalizes an ea…
Local smooth convergence of -limit flows
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
The metric flow is introduced and extensively studied by Bamler [Bam20b, Bam20c], especially as an -limit of a sequence of smooth Ricci flows with uniformly bounded Nas…