Discrete Approximations of Metric Measure Spaces of Controlled Geometry
Metric Geometry
2015-05-12 v2
Abstract
We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poincare inequalities on graphs.
Keywords
Cite
@article{arxiv.1408.2132,
title = {Discrete Approximations of Metric Measure Spaces of Controlled Geometry},
author = {James T. Gill and Marcos Lopez},
journal= {arXiv preprint arXiv:1408.2132},
year = {2015}
}
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23 Pages