A characteristic-index inequality for closed embeddings of locally compact groups

局部紧群及其闭子群的Young卷积不等式最优常数的不等式

Inequality on the optimal constant of Young's convolution inequality for locally compact groups and their closed subgroups

该研究定义了局部紧群上Young卷积不等式的最优常数，证明其对闭子群的不等式关系，并推导出一类连通李群的最优常数上界。

An inequality for the convolutions on unimodular locally compact groups and the optimal constant of Young's inequality

Let $μ$ be the Haar measure of a unimodular locally compact group $G$ and $m (G)$ as the infimum of the volumes of all open subgroups of $G$. The main result of this paper is that \begin{align*} \int_{G}^{} f \circ \left( ϕ_1 * ϕ_2 \right) \left( g \right) dg \leq \int_{\mathbb{R}}^{} f \circ \left( ϕ_1^* * ϕ_2^* \right) \left( x \right) dx \end{align*} holds for any measurable functions $ϕ_1, ϕ_2 \colon G \to \mathbb{R}_{\geq 0}$ with $μ( \mathrm{supp} \; ϕ_1 ) + μ( \mathrm{supp} \; ϕ_2 ) \leq m(G)$ and any convex function $f \colon \mathbb{R}_{\geq 0} \to \mathbb{R}$ with $f(0) = 0$. Here $ϕ…

非阿贝尔Brunn-Minkowski不等式

A nonabelian Brunn-Minkowski inequality

该研究将Brunn-Minkowski不等式推广到非阿贝尔局部紧群，证明其对无螺旋群（含实线性代数群、半单Lie群等）成立且锐利，采用维数归纳、最大紧子群分析和按比例平均技巧。

非阿贝尔布伦-闵可夫斯基不等式 II

A nonabelian Brunn-Minkowski inequality II

该研究证明非紧李维数为n的单模局部紧群满足严格非阿贝尔布伦-闵可夫斯基不等式，建立了一般形式并证实相关猜想，还应用得到非紧型对称空间的等周不等式。

Locally Random Groups

In this work, we will introduce and study the notion of local randomness for compact metric groups. We prove a mixing inequality as well as a product result for locally random groups under an additional dimension condition on the volume of small balls and provide several examples of such groups. In particular, this leads to new examples of groups satisfying such a mixing inequality. In the same context, we will develop a Littlewood-Paley decomposition and explore its connection to the existence of the spectral gap for random walks. Moreover, under the dimension condition alone, we will prove a…

由有序集索引的拓扑单无限矩阵群

Topologically simple infinite matrix groups indexed by ordered sets

本文从拓扑角度研究有序集索引的关联环单位群，明确其继承拓扑结构的条件，用拓扑域上无限矩阵群构造拓扑单矩阵群并推广已有结果，还建立了其与初等完全不连通局部紧群的联系。