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arXiv · 1907.11016

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

Francesco Boarotto·Roberto Monti·Francesco Palmurella
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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.

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Francesco Boarotto, Roberto Monti, Francesco Palmurella. 2019-07-25. Third order open mapping theorems and applications to the end-point map. https://doi.org/10.1088/1361-6544%2Fab8bad

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