Direct embeddings of relatively hyperbolic groups with optimal $\ell^p$ compression exponent

Elliptic, Parabolic and Hyperbolic Analytic Function Theory--0: Geometry of Domains

This paper lays down a foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theory based on the representation theory of SL(2,R) group. We describe here geometries of corresponding domains. The principal role is played by Clifford algebras of matching types. Keywords: analytic function theory, semisimple groups, elliptic, parabolic, hyperbolic, Clifford algebras

一致Lipschitz双曲群在$\ell^p$上的作用

Uniformly Lipschitz Hyperbolic Group Actions on $\ell^p$

本文证明有限生成双曲群在$\ell^p$上存在压缩指数为$1/p$的恰当一致Lipschitz仿射作用，其中$p<Q/(Q-1)$，空间由边界填充上的马尔可夫链构造。

双曲椭圆抛物盘的半距离带近似

Hyperbolic elliptic parabolic disks approximated by half distance bands

本文研究双曲椭圆抛物盘在双曲几何中的描述方法，并探讨其与支撑半距离带的精确近似关系。

Hyperbolic group $C^*$-algebras and free-product $C^*$-algebras as compact quantum metric spaces

Let $\ell$ be a length function on a group G, and let $M_{\ell}$ denote the operator of pointwise multiplication by $\ell$ on $\bell^2(G)$. Following Connes, $M_{\ell}$ can be used as a ``Dirac'' operator for $C_r^*(G)$. It defines a Lipschitz seminorm on $C_r^*(G)$, which defines a metric on the state space of $C_r^*(G)$. We show that if G is a hyperbolic group and if $\ell$ is a word-length function on G, then the topology from this metric coincides with the weak-* topology (our definition of a ``compact quantum metric space''). We show that a convenient framework is that of filtered $C^*$-a…

将树拟合到 $\ell_1$-双曲距离

Fitting trees to $\ell_1$-hyperbolic distances

本文研究将树拟合到距离的问题，通过定义双曲性向量的 $\ell_1$ 范数并提出算法 HCCRootedTreeFit，给出了树嵌入误差的紧致解析界，并揭示标准层次数据集与真正树状数据集的树拟合存在根本差异。