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

@inproceedings{Boarotto2019ThirdOO,
  title={Third order open mapping theorems and applications to the end-point map},
  author={Francesco Boarotto and Roberto Monti and Francesco Palmurella},
  year={2019}
}
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… CONTINUE READING