On the codimension of the abnormal set in step two Carnot groups

DOI10.1051/cocv/2018002zbMath1444.53024arXiv1709.02854OpenAlexW2962753103MaRDI QIDQ5107921

Davide Vittone, Alessandro Ottazzi

Publication date: 29 April 2020

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.02854

zbMATH Keywords

sub-Riemannian geometryabnormal curvesCarnot groupsendpoint mapSard property

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Nilpotent and solvable Lie groups (22E25) Sub-Riemannian geometry (53C17)

Related Items (4)

The Sard problem in step 2 and in filiform Carnot groups, ⋮ A dynamical approach to the Sard problem in Carnot groups ⋮ Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry ⋮ Universal differentiability sets in Carnot groups of arbitrarily high step

Cites Work

• Sard property for the endpoint map on some Carnot groups
• Any sub-Riemannian metric has points of smoothness
• Morse-Sard type results in sub-Riemannian geometry
• Geodesics and horizontal-path spaces in Carnot groups
• Some open problems
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