Liouville’s theorem says that in dimension greater than two, all conformal maps are Möbius transformations. We prove an analogous statement about simplicial complexes, where two simplicial complexes are considered discretely conformally equivalent if they are combinatorially equivalent and the lengths of corresponding edges are related by scale factors associated with the vertices.

中文翻译：

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共形图中Liouville定理的离散形式

Liouville定理说，在大于2的维度上，所有共形图都是Möbius变换。我们证明了一个关于单纯形复形的类似陈述，其中两个单纯形复形在组合上相等时被视为离散共形等效，并且相应边的长度由与顶点相关的比例因子相关。