Work

Universal differentiability sets and maximal directional derivatives in Carnot groups

Year: 2017

Type: preprint

Abstract: We show that every Carnot group G of step 2 admits a Hausdorff dimension one `universal differentiability set' N such that every real-valued Lipschitz map on G 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1705.05871

Authors: Donne, Enrico Le, Pinamonti, Andrea, Speight, Gareth

Institution: University of Jyväskylä

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4297908846

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