On the noncollapsedness of positively curved Type I ancient Ricci flows

带边界曲面上正曲率 ancient Ricci 流的唯一性

Uniqueness of positively curved ancient Ricci flows on surfaces with boundary

本文证明了满足直径一致有界、边界测地曲率为正常数的二维带边界曲面上正曲率 ancient Ricci 流的存在与唯一性，该流具旋转对称性，其极限行为明确，是带边界 ancient Ricci 流分类的首个结果。

Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry

We study harmonic map heat flow along ancient super Ricci flow, and derive several Liouville theorems with controlled growth from Perelman's reduced geometric viewpoint. For non-positively curved target spaces, our growth condition is sharp. For positively curved target spaces, our Liouville theorem is new even in the static case (i.e., for harmonic maps); moreover, we point out that the growth condition can be improved, and almost sharp in the static case. This fills the gap between the Liouville theorem of Choi and the example constructed by Schoen-Uhlenbeck.

非负曲率的古老里奇流

Ancient Ricci flows with nonnegative Ricci curvature

本文研究了非负曲率非塌陷古老里奇流的渐近几何，通过其无穷远处的非塌陷F-极限度量孤子得出两个分歧定理。

具有正夹挤Ricci曲率的完备Riemann流形是否是紧的

Is a complete Riemannian manifold with positively pinched Ricci curvature compact

本文针对Hamilton关于欧氏空间中带夹挤第二基本形式的凸超曲面必为紧集的结果，利用作者1998年的拟共形映射结论给出无需额外假设的完整替代证明且可推广，以此纪念Ricci流创立者Hamilton。

An equation linking $\mathscr{W}$-entropy with reduced volume

$\mathscr{W}$-entropy and reduced volume for the Ricci flow were introduced by Perelman, which had proved their importance in the study of the Ricci flow. L. Ni studied the analogous concepts for the linear heat equation on the static manifolds, and established an equation which links the large time behavior of these two. Due to the surprising similarity between those concepts in the Ricci flow and the linear heat equation, a natural question whether such equation holds for the Ricci flow ancient solution was asked by L. Ni. In this paper, we gave an alternative proof to L. Ni's original equat…