We consider a finitely generated group endowed with a word metric. The group acts on itself by isometries, which induces an action on its horofunction boundary. The conjecture is that nilpotent groups act trivially on their reduced boundary. We will show this for the Heisenberg group. The main tool will be a discrete version of the isoperimetric inequality.

中文翻译：

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关于离散海森堡群的水平函数边界

我们考虑具有词度量的有限生成组。该组通过等距作用于自身，从而在其水平功能边界上产生作用。猜想是幂零群在其缩减边界上的作用微不足道。我们将为海森堡集团展示这一点。主要工具将是等周不等式的离散版本。