Abstract We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality. Then we apply this to show that quasiconformal mappings can be characterized by the fact that they quasi-preserve the modulus of certain families of surfaces.

中文翻译：

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度量空间中模映射和拟共形映射的对偶性

摘要 我们证明了连接两个集合的曲线族和分隔集合的曲面族的模的对偶关系，在一个完整的度量空间的设置下，该空间配备了加倍测度并支持庞加莱不等式。然后我们应用它来表明准共形映射的特征在于它们准保留某些表面族的模量。