# Structure of porous sets in Carnot groups

@article{Pinamonti2016StructureOP,
title={Structure of porous sets in Carnot groups},
author={A. Pinamonti and G. Speight},
journal={Illinois Journal of Mathematics},
year={2016},
volume={61},
pages={127-150}
}
• Published 2016
• Mathematics
• Illinois Journal of Mathematics
A set is porous if each point sees relatively large holes in the set on arbitrarily small scales. We show that sets porous with respect to the Carnot-Carath\'eodory distance are much smaller than measure zero sets and are not comparable with sets porous with respect to the Euclidean distance. We construct a Lipschitz function which is Pansu differentiable at no point of a given sigma-porous set and show preimages of open sets under the horizontal gradient are far from being porous.
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