A Hadamard-type open map theorem for submersions and applications to completeness results in Control Theory
Classical Analysis and ODEs
2015-01-28 v2 Differential Geometry
Abstract
We prove a quantitative openness theorem for 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.
Keywords
Cite
@article{arxiv.1408.3707,
title = {A Hadamard-type open map theorem for submersions and applications to completeness results in Control Theory},
author = {Andrea Bonfiglioli and Annamaria Montanari and Daniele Morbidelli},
journal= {arXiv preprint arXiv:1408.3707},
year = {2015}
}
Comments
12 pages. Revised version. Minor changes. To appear on Annali di Matematica