Communications in Analysis and Geometry
Volume 26 (2018)
Extremal polynomials in stratified groups
Pages: 723 – 757
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal sub-Riemannian extremals in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations, in both normal and abnormal case.
abnormal extremals, extremal polynomials, Carnot groups, sub-Riemannian geometry
This work was partially supported by the INDAM, University of Padova research project “Some analytic and differential geometric aspects in Nonlinear Control Theory, with applications to Mechanics”; and by the Fondazione CaRiPaRo Project “Nonlinear Partial Differential Equations: models, analysis, and control-theoretic problems”.
Received 1 February 2015