Calculus of Variations and Geometric Measure Theory

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

Extremal polynomials in stratified groups

created by vittone on 19 Jul 2013
modified on 17 Nov 2020


Published Paper

Inserted: 19 jul 2013
Last Updated: 17 nov 2020

Journal: Comm. Anal. and Geom.
Volume: 26
Pages: 723–757
Year: 2018


We introduce a family of extremal polynomial associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.

Keywords: Carnot groups, SubRiemannian geometry, Abnormal extremals, Extremal polynomials