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Unrectifiable surfaces with intrinsic regularity in Carnot groups
In any noncommutative Carnot group, for every $0\le α<1$, we show the existence of a $C^{1,α}_\mathrm H$ surface that is unrectifiable with respect to the Euclidean distance. Precisely, the surface has Euclidean Hausdorff dimension higher than its topological dimension. We show that in step-2 Carnot
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