Universal differentiability sets and maximal directional derivatives in Carnot groups
Le Donne, E., Pinamonti, A., & Speight, G. (2019). Universal differentiability sets and maximal directional derivatives in Carnot groups. Journal de Mathematiques Pures et Appliquees, 121, 83-112. https://doi.org/10.1016/j.matpur.2017.11.006
Published inJournal de Mathematiques Pures et Appliquees
© 2017 Elsevier Masson SAS.
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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Related funder(s)Academy of Finland; European Commission
Funding program(s)Research post as Academy Research Fellow, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingE.L.D. is supported by the Academy of Finland grant 288501 and by the ERC Starting Grant 713998 GeoMeG. A.P. acknowledges the support of the Istituto Nazionale di Alta Matematica F. Severi. G.S. received support from the Charles Phelps Taft Research Center.
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