Third order open mapping theorems and applications to the end-point map
Differential Geometry
2022-05-09 v1 Classical Analysis and ODEs
Optimization and Control
Abstract
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 space into 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.
Keywords
Cite
@article{arxiv.1907.11016,
title = {Third order open mapping theorems and applications to the end-point map},
author = {Francesco Boarotto and Roberto Monti and Francesco Palmurella},
journal= {arXiv preprint arXiv:1907.11016},
year = {2022}
}