We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups.
@article{bwmeta1.element.doi-10_1515_agms-2015-0001,
author = {Piotr Haj\l asz and Soheil Malekzadeh},
title = {On Conditions for Unrectifiability of a Metric Space},
journal = {Analysis and Geometry in Metric Spaces},
volume = {3},
year = {2015},
zbl = {1321.28008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0001}
}
Piotr Hajłasz; Soheil Malekzadeh. On Conditions for Unrectifiability of a Metric Space. Analysis and Geometry in Metric Spaces, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2015-0001/
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