7 citations · 24 across the 20 of their papers we have counts for
21 papers · 1 filter
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…
Gap Theorem on Riemannian manifolds using Ricci flow
Pak-Yeung Chan, Man-Chun Lee
In this work, we use the Ricci flow approach to study the gap phenomenon of Riemannian manifolds with non-negative curvature and sub-critical scaling invariant curvature decay. The…
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…
Manifolds with small curvature concentration
Pak-Yeung Chan, Shaochuang Huang, Man-Chun Lee
In this work, we construct distance like functions with integral hessian bound on manifolds with small curvature concentration and use it to construct Ricci flows on manifolds with…
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…
On a dichotomy of the curvature decay of steady Ricci soliton
Pak-Yeung Chan, Bo Zhu
We establish a dichotomy on the curvature decay for four dimensional complete noncompact non Ricci flat steady gradient Ricci soliton with linear curvature decay and proper potenti…
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.…
Small curvature concentration and Ricci flow smoothing
Pak-Yeung Chan, Eric Chen, Man-Chun Lee
We show that a complete Ricci flow of bounded curvature which begins from a manifold with a Ricci lower bound, local entropy bound, and small local scale-invariant integral curvatu…
Curvature estimates and gap theorems for expanding Ricci solitons
Pak-Yeung Chan
We derive a sharp lower bound for the scalar curvature of non-flat and non-compact expanding gradient Ricci soliton provided that the scalar curvature is non-negative and the poten…
Curvature estimates for steady Ricci solitons
Pak-Yeung Chan
We show that for an dimensional complete non Ricci flat gradient steady Ricci soliton with potential function bounded above by a constant and curvature tensor satisfyi…
Gradient steady Kahler Ricci solitons with non-negative Ricci curvature and integrable scalar curvature
Pak-Yeung Chan
We study the non Ricci flat gradient steady Kähler Ricci soliton with non-negative Ricci curvature and weak integrability condition of the scalar curvature , namely $\underline{…
A note on center of mass
Pak-Yeung Chan, Luen-Fai Tam
We will discuss existence of center of mass on asymptotically Schwarzschild manifold defined by Huisken-Yau and Corvino-Schoen. Conditions of existence and examples on non existenc…