291 research outputs found
On conditions for unrectifiability of a metric space
We find necessary and sufficient conditions for a Lipschitz map
, into a metric space to have the image with the
-dimensional Hausdorff measure equal zero, . 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
and that of more general Carnot-Carath\'eodory spaces
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