Calculus of Variations and Geometric Measure Theory

E. Le Donne - G. P. Leonardi - R. Monti - D. Vittone

Extremal curves in nilpotent Lie groups

created by vittone on 17 Jul 2012
modified on 25 Jul 2017


Published Paper

Inserted: 17 jul 2012
Last Updated: 25 jul 2017

Journal: GAFA Geometric and Functional Analysis
Volume: 23
Number: 4
Pages: 1371--1401
Year: 2013


We classify extremal curves in free nilpotent Lie groups. The classi fication is obtained via an explicit integration of the adjoint equation in Pontryagin Maximum Principle. It turns out that abnormal extremals are precisely the horizontal curves contained in algebraic varieties of a speci c type. We also extend the results to the nonfree case.

Keywords: Carnot groups, Regularity of geodesics, Abnormal curves, Extremal curves, Free nilpotent groups, SubRiemannian geometry, Algebraic variety