Geodesic
On Conditions for Unrectifiability of a Metric Space
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

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.
Mots-clés : geometric measure theory, unrectifiability, metric spaces, Sard theorem, Carnot-Carathéodoryspaces 
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     author = {Haj{\l}asz, Piotr and Malekzadeh, Soheil},
     title = {On {Conditions} for {Unrectifiability} of a {Metric} {Space}},
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Hajłasz, Piotr; Malekzadeh, Soheil. On Conditions for Unrectifiability of a Metric Space. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a17/