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arXiv · 1408.3707

A Hadamard-type open map theorem for submersions and applications to completeness results in Control Theory

Andrea Bonfiglioli·Annamaria Montanari·Daniele Morbidelli
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Abstract

We prove a quantitative openness theorem for $C^1$ submersions under suitable assumptions on the differential. We then apply our result to a class of exponential maps appearing in Carnot-Carath\'eodory spaces and we improve a classical completeness result by Palais.

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Andrea Bonfiglioli, Annamaria Montanari, Daniele Morbidelli. 2014-08-16. A Hadamard-type open map theorem for submersions and applications to completeness results in Control Theory. https://doi.org/10.1007/s10231-014-0471-x

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