Metric Differentiation, Monotonicity and Maps to L
نویسندگان
چکیده
We present a new approach to the infinitesimal structure of Lipschitz maps into L, and as an application, we give an alternative proof of the main theorem of [CK06], that the Heisenberg group does not admit a bi-Lipschitz embedding in L. The proof uses the metric differentiation theorem of [Pau01] and the cut metric description in [CK06] to reduce the nonembedding argument to a classification of monotone subsets of the Heisenberg group.
منابع مشابه
A ug 2 00 9 METRIC DIFFERENTIATION , MONOTONICITY AND MAPS TO L 1
This is one of a series of papers on Lipschitz maps from metric spaces to L. Here we present the details of results which were announced in [CK06, Section 1.8]: a new approach to the infinitesimal structure of Lipschitz maps into L, and, as a first application, an alternative proof of the main theorem of [CK06], that the Heisenberg group does not admit a bi-Lipschitz embedding in L. The proof u...
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