Calculus of Variations and Geometric Measure Theory

F. Boarotto - R. Monti - F. Palmurella

Third order open mapping theorems and applications to the end-point map

created by monti on 20 Sep 2019
modified by palmurella on 06 May 2022


Published Paper

Inserted: 20 sep 2019
Last Updated: 6 may 2022

Journal: Nonlinearity
Volume: 33
Number: 9
Pages: 4539-4567
Year: 2020
Doi: 10.1088/1361-6544/ab8bad


This paper is devoted to a third order study of the end-point map in sub-Riemannian geometry. We first prove third order open mapping results for maps from a Banach spaceinto a finite dimensional manifold. In a second step, we compute the third order term in the Taylor expansion of the end-point map and we specialize the abstract theory to the study of length-minimality of sub-Riemannian strictly singular curves. We conclude with the third order analysis of a specific strictly singular extremal that is not length-minimizing.