Quasicircles and Bounded Turning Circles Modulo bi-Lipschitz Maps
Quasicircles and Bounded Turning Circles Modulo bi-Lipschitz Maps
复制标题
拟圆和有界回转圆模 bi-Lipschitz 映射
DOI：
10.4171/rmi/687
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Daniel Meyer
中科院分区：
文献类型：
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作者：
D. Herron;Daniel Meyer
我们构建了一个目录，雪花型度量圆，描述了所有的度量拟圆的\BL\等价。这是一个度量空间模拟的结果，由于罗德。我们的构造也适用于所有有界转动的度量圆;这些圆不需要加倍。作为一个副产品，我们表明，度量拟圆的Assouad维数严格小于2是bi-Lipschitz等价于一个平面拟圆。
We construct a catalog, of snowflake type metric circles, that describes all metric quasicircles up to \bl\ equivalence. This is a metric space analog of a result due to Rohde. Our construction also works for all bounded turning metric circles; these need not be doubling. As a byproduct, we show that a metric quasicircle with Assouad dimension strictly less than two is bi-Lipschitz equivalent to a planar quasicircle.