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Memoirs of the American Mathematical Society
1996; 104 pp; softcover
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Order Code: MEMO/118/564
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.
Graduate students, mathematicians, physicists, engineers interested in geometry, optimal control theory, or the calculus of variations.
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