8 papers
Volume growth and integral curvature bound for non-negatively curved three-manifolds
Pak-Yeung Chan, Man-Chun Lee, Mingxiang Li
Motivated by results in Kähler geometry, in this work, we are interested in understanding the relation between integral curvature bounds and volume growth, under non-negative curva…
Rigidity and gap theorems for Ricci shrinkers
Pak-Yeung Chan, Yongjia Zhang
We prove local versions of the Ricci curvature and -entropy gap theorems for Ricci shrinkers, which respectively generalize a previous result of Munteanu-Wang and a prior result…
Curvature estimates for steady and expanding solitons in higher dimensions
Pak-Yeung Chan, Ming Hsiao
In this paper, we demonstrate certain curvature estimates on complete non-compact steady and expanding gradient Ricci solitons in higher dimensions. In the expanding case, we prove…
Higher-dimensional flying wing Steady Ricci Solitons
Pak-Yeung Chan, Yi Lai, Man-Chun Lee
For any , we construct an -parameter family of steady gradient Ricci solitons with non-negative curvature operator and prescribed by the eigenvalues of Ricci tensor…
On the weakly conical expanding gradient Ricci solitons
Pak-Yeung Chan, Man-Chun Lee
In this work, we construct several sequences of metrics on sphere with different limiting behaviors. By combining with the work of Deruelle, we use it and the localized maximum pri…
Expanding Ricci solitons coming out of weakly PIC1 metric cones
Pak-Yeung Chan, Man-Chun Lee, Luke T. Peachey
Motivated by recent work of Deruelle-Schulze-Simon, we study complete weakly PIC1 Ricci flows with Euclidean volume growth coming out of metric cones. We show that such a Ricci flo…
A family of Kähler flying wing steady Ricci solitons
Pak-Yeung Chan, Ronan J. Conlon, Yi Lai
In , H.-D. Cao constructed a -invariant steady gradient Kähler-Ricci soliton on and asked whether every steady gradient Kähler-Ricci soliton of positiv…
Gap Theorem on manifolds with small curvature concentration
Pak-Yeung Chan, Man-Chun Lee
In this work, we show that complete non-compact manifolds with non-negative Ricci curvature, Euclidean volume growth and sufficiently small curvature concentration are necessarily…