Communications in Analysis and Geometry

Volume 26 (2018)

Number 4

Extremal polynomials in stratified groups

Pages: 723 – 757



Enrico Le Donne (Department of Mathematics and Statistics, University of Jyväskylä, Finland)

Gian Paolo Leonardi (Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Modena, Italy)

Roberto Monti (Dipartimento di Matematica, Università di Padova, Italy)

Davide Vittone (Dipartimento di Matematica, Università di Padova, Italy)


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

Published 6 September 2018