7 citations · 24 across the 17 of their papers we have counts for
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Hamilton-Ivey estimates for gradient Ricci solitons
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
We first show that any -dimensional non-Ricci-flat steady gradient Ricci soliton singularity model must satisfy for some positive constant . Then, we apply the…
A local Sobolev inequality on Ricci flow and its applications
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
In this article, we prove a local Sobolev inequality for complete Ricci flows. Our main result is that the local -functional of a disk on a Ricci flow depends only on the Nash e…
An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons
Richard H. Bamler, Pak-Yeung Chan, Zilu Ma +1
In this paper, we prove a volume growth estimate for steady gradient Ricci solitons with bounded Nash entropy. We show that such a steady gradient Ricci soliton has volume growth r…
On Ricci flows with closed and smooth tangent flows
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
In this paper, we consider Ricci flows admitting closed and smooth tangent flows in the sense of Bamler [Bam20c]. The tangent flow in question can be either a tangent flow at infin…
A uniform Sobolev inequality for ancient Ricci flows with bounded Nash entropy
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
This note is a continuation of [CMZ21]. We shall show that an ancient Ricci flow with uniformly bounded Nash entropy must also have uniformly bounded -functional. Consequently,…
Ancient Ricci flows with asymptotic solitons
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
We study ancient Ricci flows which admit asymptotic solitons in the sense of Perelman. We prove that the asymptotic solitons must coincide with Bamler's tangent flows at infinity.…
Four-Dimensional Steady Gradient Ricci Solitons with -Cylindrical Tangent Flows at Infinity
Richard Bamler, Bennett Chow, Yuxing Deng +2
In this paper we consider -dimensional steady soliton singularity models, i.e., complete steady gradient Ricci solitons that arise as the rescaled limit of a finite time singula…
Perelman's entropy on ancient Ricci flows
Zilu Ma, Yongjia Zhang
In [ZY2], the second author proved Perelman's assertion, namely, for an ancient Ricci flow with bounded and nonnegative curvature operator, bounded entropy is equivalent to noncoll…