度量测度空间上的等周不等式与带可加误差的Lipschitz序
Isoperimetric inequality on a metric measure space and Lipschitz order with an additive error
摘要：
M. Gromov在度量测度空间的集合上引入了Lipschitz序关系，发展了丰富的理论。特别是，他声称，一个等周不等式上的非离散空间表示使用Lipschitz秩序。我们放宽了Lipschitz序的定义，允许一个加性误差与离散空间上的一个等周不等式有关。作为应用，我们利用离散$l^1$-立方体的一个等周不等式的极限，得到了非离散$n$ -维$l^1$-立方体的一个等周不等式.
英文摘要：
M. Gromov introduced the Lipschitz order relation on the set of metric measure spaces and developed a rich theory. In particular, he claimed that an isoperimetric inequality on a non-discrete space is represented by using the Lipschitz order. We relax the definition of the Lipschitz order allowing an additive error to relate with an isoperimetric inequality on a discrete space. As an application, we obtain an isoperimetric inequality on the non-discrete $n$-dimensional $l^1$-cube by taking the limits of an isoperimetric inequality of the discrete $l^1$-cubes.
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