Calculus of Variations and Geometric Measure Theory
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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

[BibTeX]

Published Paper

Inserted: 19 jul 2013
Last Updated: 17 nov 2020

Journal: Comm. Anal. and Geom.
Volume: 26
Pages: 723–757
Year: 2018
Doi: http://dx.doi.org/10.4310/CAG.2018.v26.n4.a3

Abstract:

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


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