度量空间中保形模的注释

Pub Date : 2022-08-25 DOI:10.7146/math.scand.a-136656

Matthew Romney

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引用次数: 0

摘要

我们给出了一个Ahlfors $3$正则，线性局部连通度量空间同纯于$\mathbb {R}^3$，其中包含一个具有零容量的非退化连续体$E$，即与$E$相交的非平凡曲线集的共形模为零。我们将这个例子与度量空间的拟共形均匀化问题联系起来讨论。

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Remarks on conformal modulus in metric spaces

We give an example of an Ahlfors $3$-regular, linearly locally connected metric space homeomorphic to $\mathbb {R}^3$ containing a nondegenerate continuum $E$ with zero capacity, in the sense that the conformal modulus of the set of nontrivial curves intersecting $E$ is zero. We discuss this example in relation to the quasiconformal uniformization problem for metric spaces.

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