every quadratically rigid trajectory is a strict strong length minimizer
for any choice
of strictly convex submetric on the distribution.
(Actually, the submetric can possess a certain weaker property than its strict convexity.)
This strengthens the known results of other authors (Montgomery, Liu-Sussmann, Petrov, and Agrachev-Sarychev).
Also, similar results are obtained for arbitrary nonstrictly convex submetrics. In this case our conditions guarantee not
the strong minimality, but the L_1-minimality of the trajectory w.r.t. the velocity. Both these results are valid for
distributions of arbitrary dimension and for trajectories of arbitrary length (not only for their small pieces).
Russian original:
Квадратичные достаточные условия сильной минимальности анормальных
субримановых геодезических -- Итоги науки и техники. Современная мат-ка и ее приложения, т. 65
(Труды конференции, посвященной 90-летию Л.С.Понтрягина,
т. 4, Оптимальное управление),
М., 2000, с. 5—89.
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