Communications in Analysis and Geometry

Volume 26 (2018)

Number 4

Extremal polynomials in stratified groups

Pages: 723 – 757

DOI: https://dx.doi.org/10.4310/CAG.2018.v26.n4.a3

Authors

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)

Abstract

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.

Keywords

abnormal extremals, extremal polynomials, Carnot groups, sub-Riemannian geometry

Full Text (PDF format)

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