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Published online by Cambridge University Press: 28 October 2019
This chapter is devoted to the analysis of thesecond-order conditions for length-minimizers andthe analysis of abnormal extremals. After a firstresult on the regularity of the squaredsub-Riemannian distance from a fixed point, showingthat Lipschitz regularity is lost at those pointsreached by only abnormal length-minimizers, we moveto second-order conditions, known as the Goh andgeneralized Legendre conditions.
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