13 citations · 42 across the 28 of their papers we have counts for
30 papers
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…
Kählerity of Einstein four-manifolds
Xiaolong Li, Yongjia Zhang
We prove that a closed oriented Einstein four-manifold is either anti-self-dual or (after passing to a double Riemann cover if necessary) Kähler-Einstein, provided that $λ_2 \geq -…
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…
Canonical surgeries in rotationally invariant Ricci flow
Timothy Buttsworth, Maximilien Hallgren, Yongjia Zhang
We construct a rotationally invariant Ricci flow through surgery starting at any closed rotationally invariant Riemannian manifold. We demonstrate that a sequence of such Ricci flo…
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…
Pseudolocality and uniqueness of Ricci flow on almost Euclidean noncompact manifolds
Liang Cheng, Yongjia Zhang
In this paper, we prove a pseudolocality-type theorem for -complete noncompact Ricci flow which may not have bounded sectional curvature; with the help of it we study t…
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…
No breather theorems for the mean curvature flow
Liang Cheng, Yongjia Zhang
In this article we study the breathers of the mean curvature flow in the Euclidean space. A breather is a solution to the mean curvature flow which repeats itself up to isometry an…
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.…
A no expanding breather theorem for noncompact Ricci flows
Liang Cheng, Yongjia Zhang
In this note we show that, under certain curvature positivity conditions (the weak condition or the nonnegative bisectional curvature condition), a complete…
On the noncollapsedness of positively curved Type I ancient Ricci flows
Liang Cheng, Yongjia Zhang
In this article, we study complete Type I ancient Ricci flows with positive sectional curvature. Our main results are as follows: in the complete and noncompact case, all such anci…
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…
Manifolds with positive curvature operator and strictly convex bounday
Yongjia Zhang
In [AMW], it is proved that if a compact -manifold has positive Ricci curvature and strictly convex boundary, then this manifold is diffeomorphic to the standard -dimensional…
Perelman-type no breather theorem for noncompact Ricci flows
Liang Cheng, Yongjia Zhang
In this paper, we first show that a complete shrinking breather with Ricci curvature bounded from below must be a shrinking gradient Ricci soliton. This result has several applicat…
Curvature growth of some 4-dimensional gradient Ricci soliton singularity models
Bennett Chow, Michael Freedman, Henry Shin +1
In this note we discuss estimates for the curvature of 4-dimensional gradient Ricci soliton singularity models by applying Perelman's point selection, a fundamental result of Cheeg…
Ancient solutions to the Ricci flow in higher dimensions
Xiaolong Li, Yongjia Zhang
In this paper, we study -noncollapsed ancient solutions to the Ricci flow with nonnegative curvature operator in higher dimensions. We impose one further assumption: one of the…
A note on Perelman's no shrinking breather theorem
Yongjia Zhang
As an application of his entropy formula, Perelman proved that every compact shrinking breather is a shrinking gradient Ricci soliton. We give a proof for the complete noncompact c…
The rigidity of under ancient Ricci flow
Yongjia Zhang
In this paper we generalize the neck-stability theorem of Kleiner-Lott to a special class of four-dimensional nonnegatively curved Type I -solutions, namely, those whose asympto…