7 citations · 24 across the 17 of their papers we have counts for
18 papers
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…
A local gap theorem for Ricci shrinkers
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
We prove a local gap theorem for Ricci shrinkers, which states that if the local -functional at scale on a large ball centered at the minimum point of the potential function…
Lower bounds for the scalar curvatures of Ricci flow singularity models
Pak-Yeung Chan, Bennett Chow, Zilu Ma +1
In a series of papers, Bamler [Bam20a,Bam20b,Bam20c] further developed the high-dimensional theory of Hamilton's Ricci flow to include new monotonicity formulas, a completely gener…
Volume growth estimates of gradient Ricci solitons
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
In this paper, we survey the volume growth estimates for shrinking, steady, and expanding gradient Ricci solitons. Together with the known results, we also prove some new volume gr…
The rate of -convergence for Ricci flows with closed and smooth tangent flows
Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
This article is a continuation of [CMZ21b], where we proved that a Ricci flow with a closed and smooth tangent flow has unique tangent flow, and its corresponding forward or backwa…
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…
On Four-dimensional Steady gradient Ricci solitons that dimension reduce
Bennett Chow, Yuxing Deng, Zilu Ma
In this paper, we will study the asymptotic geometry of 4-dimensional steady gradient Ricci solitons under the condition that they dimension reduce to -manifolds. We will show t…
Understanding Self-Paced Learning under Concave Conjugacy Theory
Shiqi Liu, Zilu Ma, Deyu Meng
By simulating the easy-to-hard learning manners of humans/animals, the learning regimes called curriculum learning~(CL) and self-paced learning~(SPL) have been recently investigate…
On Convergence Property of Implicit Self-paced Objective
Zilu Ma, Shiqi Liu, Deyu Meng
Self-paced learning (SPL) is a new methodology that simulates the learning principle of humans/animals to start learning easier aspects of a learning task, and then gradually take…