Abstract
We show that every Carnot group G of step 2 admits a Hausdorff dimension one ‘universal differentiability set’ N such that every Lipschitz map f:G→R is Pansu differentiable at some point of N. This relies on the fact that existence of a maximal directional derivative of f at a point x implies Pansu differentiability at the same point x. We show that such an implication holds in Carnot groups of step 2 but fails in the Engel group which has step 3.
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