3 papers
math.DG2026
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…
math.DG2026
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}…
math.DG2025
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 r…