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On Conditions for Unrectifiability of a Metric Space

Piotr HajłaszSoheil Malekzadeh — 2015

Analysis and Geometry in Metric Spaces

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.

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