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arXiv · 1902.07424

Isoperimetric inequality on a metric measure space and Lipschitz order with an additive error

Hiroki Nakajima
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Abstract

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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Hiroki Nakajima. 2019-02-20. Isoperimetric inequality on a metric measure space and Lipschitz order with an additive error. https://arxiv.org/abs/1902.07424

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