Geometric and analytic quasiconformality in metric measure spaces
Geometric and analytic quasiconformality in metric measure spaces
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度量测度空间中的几何和解析拟共形性
DOI：
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发表时间：
2010
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通讯作者：
Marshall Williams
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文献类型：
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作者：
Marshall Williams
我们证明了任意局部有限可分度量测度空间之间的同胚$f\colon X\rightarrow Y$的拟共形性的几何定义和解析定义之间的等价性，假设在任一空间上都没有度量假设。当$X$和$Y$具有局部$Q$-有界几何，并且$Y$包含在曲率上有界的Alexandrov空间中时，我们的结果的清晰性意味着，与经典情形一样，$\map$的模和逐点外置换通过$K_O（f）= \operatorname{esssup} H_O（x，f）$联系起来.
We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either space. When $X$ and $Y$ have locally $Q$-bounded geometry and $Y$ is contained in an Alexandrov space of curvature bounded above, the sharpness of our results implies that, as in the classical case, the modular and pointwise outer dilatations of $\map$ are related by $K_O(f)= \operatorname{esssup} H_O(x,f)$.