A mountain-pass theorem for asymptotically conical self-expanders

渐近锥形梯度Kähler-Ricci扩张子的稳定性

Stability of asymptotically conical gradient Kähler-Ricci expanders

本文证明渐近锥形梯度Kähler-Ricci扩张子在适当扰动下，规范化Kähler-Ricci流全局存在并收敛到同类的孤子度量，且若扰动在无穷远处渐近于原度量，则极限度量与原度量相同。

扩张子泛函的单调Morse流线的存在性

Existence of monotone Morse flow lines of the expander functional

针对严格不稳定的光滑渐近锥形自扩张子，构造了连接其与稳定自扩张子的单调奇异Morse流线，该流线奇异集小，证明了扩张子泛函单调Morse流线的存在性。

A Uniqueness Result for Self-expanders with Small Entropy

In this short note, we prove a uniqueness result for small entropy self-expanders asymptotic to a fixed cone. This is a direct consequence of the mountain-pass theorem and the integer degree argument proved by J. Bernstein and L. Wang.

4维渐近锥形梯度扩张孤子的度理论

Degree theory for 4-dimensional asymptotically conical gradient expanding solitons

本文为4维渐近锥形梯度扩张孤子建立新度理论，证明对任意非负标量曲率锥存在此类孤子，并引入扩张子度不变量，揭示梯度与非梯度孤子的连通性关系。

渐近锥形高余维自收缩子与自扩张子的唯一性

Uniqueness of Asymptotically Conical Higher Codimension Self-Shrinkers and Self-Expanders

本文证明了渐近于同一锥的高余维自收缩子唯一且以单位重数收敛，并给出自扩张子在此条件下像重合的唯一性结果。

锥端漂移拉普拉斯算子概本征函数的渐近结构

Asymptotic structure of almost eigenfunctions of drift Laplacians on conical ends

我们使用的加权变体的频率函数介绍Almgren证明尖锐的渐近估计几乎本征函数的漂移拉普拉斯相关的高斯权重的渐近圆锥形结束。作为结果，我们得到了L的一个结果的纯椭圆证明。Wang关于渐近于给定锥的中曲率流的自收缩的唯一性。另一个结果是一个独特的连续性的自膨胀的中曲率流从一个圆锥。

Asymptotic Behavior and Stability of Mean Curvature Flow with a Conical End

If the initial hypersurface of an immortal mean curvature flow is asymptotic to a regular cone whose entropy is small, the flow will become asymptotically self-expanding. Moreover, the expander that gives rise to the limiting flow is asymptotically stable as an equilibrium solution of the normalized mean curvature flow.

渐近锥形梯度扩展里奇溶剂的曲率捏紧

Curvature pinching of asymptotically conical gradient expanding Ricci solitons

本文研究了完整非紧致渐近锥形梯度扩展里奇溶剂的曲率捏紧现象，建立了若干Hamilton-Ivey型曲率捏紧估计，包括三维梯度里奇扩展体的正截面曲率结果。