Lattices in R^2 and finite subsets of a circle

The third symmetric potency of the circle and the Barnette sphere

We give an elementary (not cut just paste) proof of results of Bott and Shchepin: the space of non-empty subsets of a circle of cardinality at most 3, which is called the third symmetric potency of the circle, is homeomorphic to a 3-sphere and the inclusion of the space of one element subsets is a trefoil knot. Moreover, we give an explicit simplicial decomposition of the third symmetric potency of the circle which is isomorphic to the Barnette sphere.

具有拟圆周理想边界的反德西特空间凸子集上的预定度量

The Prescribed Metric on Convex Subsets of Anti-de Sitter Space with Quasi-Circle Ideal Boundaries

本文证明给定圆盘上两个曲率受控的完备共形度量及一个拟对称映射，可构造三维反德西特空间中的全局双曲凸子集，使其未来、过去诱导度量与粘合映射均实现预定数据。

在圆上纤维化的不可约格

Irreducible lattices fibring over the circle

本文研究了不可约一致格的 BNSR 不变量，证明了在树与欧氏空间直积情形下不变量消失等价于不可约性，并构造了核的有限性由 Bestvina--Brady 群决定的不可约一致格。

无穷六边形三角剖分上Doyle圆填充的刚性

The rigidity of Doyle circle packings on the infinite hexagonal triangulation

本文针对Doyle猜想，通过发现相邻圆半径比的对数为加权离散调和函数，利用离散调和函数的Liouville定理，证明了半径比一致有界的六边形格点无穷圆填充中Doyle螺线的刚性，给出猜想的部分解答。

圆模式定理对于拟简单三角形化表面

Circle Pattern Theorem for Quasi-simplicial Triangulated Surfaces

本文将圆模式定理扩展到拟简单三角形化表面，证明在满足KAT不等式条件下，曲率映射的结构与简单情况相同，拓展了圆模式的应用范围。

论螺线管到三维空间的驯顺嵌入

On tame embeddings of solenoids into 3-space

本文研究螺线管到三维空间的驯顺嵌入，将其作为圆周驯顺嵌入的逆向极限给出分类结果，并构造出严格非手性的驯顺嵌入螺线管，揭示其与紧多面体非手性嵌入必为平面这一已知事实的鲜明对比。