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Third order open mapping theorems and applications to the end-point map
- Source :
- Nonlinearity, 33 (2020), 4539-4567
- Publication Year :
- 2019
-
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.
Details
- Database :
- arXiv
- Journal :
- Nonlinearity, 33 (2020), 4539-4567
- Publication Type :
- Report
- Accession number :
- edsarx.1907.11016
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/1361-6544/ab8bad