Assouad's theorem with dimension independent of the snowflaking
Assouad's theorem with dimension independent of the snowflaking
复制标题
维度与雪花无关的阿苏阿德定理
DOI：
10.4171/rmi/706
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Ofer Neiman
中科院分区：
文献类型：
--
作者：
A. Naor;Ofer Neiman
结果表明，对于每个$K>0$和$\e\in (0,1/2)$，都存在具有以下属性的$N=N(K)\in \N$和$D=D(K,\e)\in (1,\infty)$。对于每一个最大双倍常数的可分离度量空间$(X,d)$$K$，度量空间$(X,d^{1-\e})$允许一个双lipschitz嵌入到最大双倍常数为$D$的$\R^N$中。经典的assad嵌入定理也做出了同样的断言，但将$N\to \infty$作为$\e\to 0$。
It is shown that for every $K>0$ and $\e\in (0,1/2)$ there exist $N=N(K)\in \N$ and $D=D(K,\e)\in (1,\infty)$ with the following properties. For every separable metric space $(X,d)$ with doubling constant at most $K$, the metric space $(X,d^{1-\e})$ admits a bi-Lipschitz embedding into $\R^N$ with distortion at most $D$. The classical Assouad embedding theorem makes the same assertion, but with $N\to \infty$ as $\e\to 0$.