Metric differentiation, monotonicity and maps to L^1
Metric Geometry
2015-05-13 v2 Differential Geometry
Functional Analysis
Group Theory
Abstract
We give a new approach to the infinitesimal structure of Lipschitz maps into L^1. As a first application, we give an alternative proof of the main theorem from an earlier paper, that the Heisenberg group does not admit a bi-Lipschitz embedding in L^1. The proof uses the metric differentiation theorem of Pauls and the cut metric decomposition to reduce the nonembedding argument to a classification of monotone subsets of the Heisenberg group.
Keywords
Cite
@article{arxiv.0907.3295,
title = {Metric differentiation, monotonicity and maps to L^1},
author = {Jeff Cheeger and Bruce Kleiner},
journal= {arXiv preprint arXiv:0907.3295},
year = {2015}
}
Comments
Added a missing condition to Definition 5.3. Also made a number of minor corrections, and added a reference to a paper by Lee-Raghavendra