Shortest paths for sub-Riemannian metrics on rank-two distributions. Memoirs of the American Mathematical Society; 564.. This item is unavailable.Shortest paths for sub-Riemannian metrics on rank-two distributions. Memoirs of the American Mathematical Society; 564.

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This work studies length-minimizing arcs in sub-Riemannian manifolds $(M, E, G)$ where the metric $G$ is defined on a rank-two bracket-generating distribution $E$. The authors define a large class of abnormal extremals - the 'regular' abnormal extremals - and present an analytic technique for proving their local optimality. If $E$ satisfies a mild additional restriction-valid in particular for all regular two-dimensional distributions and for generic two-dimensional distributions - then regular abnormal extremals are 'typical,' in a sense made precise in the text. So the optimality result implies that the abnormal minimizers are ubiquitous rather than exceptional.